{
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   "source": [
    "# <center> Lecture10 : Multiple regression </center>  \n",
    " \n",
    "## <center> Instructor: Dr. Hu Chuan-Peng </center> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "tags": []
   },
   "source": [
    "## 回顾  \n",
    "\n",
    "在前面的九次课程中，我们系统性地介绍了贝叶斯统计的核心概念，并通过一个简单的线性回归模型展示了如何构建和应用一个相对简单的贝叶斯workflow。\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/smkhdwv5zt.png?imageView2/0/w/720)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "核心的知识点包括：\n",
    "\n",
    "（1）贝叶斯公式——基础：\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/skvbchkz1s.jpg?imageView2/0/w/960/h/960)  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "为了帮助大家建立关于贝叶斯推断的直觉，我们使用了三种情境：单一事件、离散变量和连续变量。 \n",
    "\n",
    "| 知识点         | 内容描述                                         | 先验                   |   似然                          | 贝叶斯更新                     |  \n",
    "|---------------|------------------------------------------------|------------------------|--------------------------------|------------------------------|  \n",
    "| **单个事件**    | 一个使用特定语言风格的心理学实验被成功重复出来的可能性  | [OSC2015](https://doi.org/10.1126/science.aac4716)的结果           |   [Herzenstein et al 2024](https://doi.org/10.1177/09567976241254037 )年的研究结果     | 可视化的方式 + 简单计算         |  \n",
    "| **离散变量**       | 多次试验(多次进行重复实验)的成功率                  | 人为分配的三种成功率(0.2, 0.5, 0.8)和它们出现的可能性  | 进行重复后的结果在**三种**成功率下出现的可能性 | 简单的手动计算 |  \n",
    "| **连续变量**       | 多次试验(多次进行重复实验)的成功率/正确率                  | 符合成功率/正确率(0~1)特点和先验经验的概率分布| 进行重复后的结果在**所有**成功率/正确率下出现的可能性 | 已被证明的统计学公式|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "在第八、九两课中，我们以一个认知实验中的研究问题——**自我和他人条件下的反应时间是否有差异**  出发，建立了一个简单的线性回归模型，并完成了贝叶斯数据分析的全流程。\n",
    "\n",
    "<p align=\"center\">\n",
    "  <img src=\"https://cdn.kesci.com/upload/smipfxtgj4.png?imageView2/0/w/640/h/640\" alt=\"Image Name\">\n",
    "</p>\n",
    "\n",
    "\n",
    "<p align=\"center\">\n",
    "  <img src=\"https://cdn.kesci.com/upload/smkijcu8co.png?imageView2/0/w/460\" alt=\"Image Name\">\n",
    "</p>\n",
    "\n",
    "> Sui, J., He, X., & Humphreys, G. W. (2012). Perceptual effects of social salience: Evidence from self-prioritization effects on perceptual matching. Journal of Experimental Psychology: Human Perception and Performance, 38(5), 1105–1117. https://doi.org/10.1037/a0029792  \n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "至此，我们可以开始进入更真实的场景，使用贝叶斯数据分析来解决一个真实的问题。\n",
    "\n",
    "第八、九两课中使用的简化数据，背后的完整数据是什么？\n",
    "\n",
    "**真实数据如下：**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# 导入 pymc 模型包，和 arviz 等分析工具 \n",
    "import pymc as pm\n",
    "import arviz as az\n",
    "import seaborn as sns\n",
    "import scipy.stats as st\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import xarray as xr\n",
    "import pandas as pd\n",
    "\n",
    "# 忽略不必要的警告\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Subject</th>\n",
       "      <th>Label</th>\n",
       "      <th>Matching</th>\n",
       "      <th>RT_sec</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>201</td>\n",
       "      <td>Self</td>\n",
       "      <td>matching</td>\n",
       "      <td>0.710595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>201</td>\n",
       "      <td>Self</td>\n",
       "      <td>nonmatching</td>\n",
       "      <td>0.739987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>201</td>\n",
       "      <td>Friend</td>\n",
       "      <td>matching</td>\n",
       "      <td>0.789074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>201</td>\n",
       "      <td>Friend</td>\n",
       "      <td>nonmatching</td>\n",
       "      <td>0.852600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>201</td>\n",
       "      <td>Stranger</td>\n",
       "      <td>matching</td>\n",
       "      <td>0.913667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>234</td>\n",
       "      <td>Self</td>\n",
       "      <td>nonmatching</td>\n",
       "      <td>0.874204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>234</td>\n",
       "      <td>Friend</td>\n",
       "      <td>matching</td>\n",
       "      <td>0.963889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>234</td>\n",
       "      <td>Friend</td>\n",
       "      <td>nonmatching</td>\n",
       "      <td>1.094103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>234</td>\n",
       "      <td>Stranger</td>\n",
       "      <td>matching</td>\n",
       "      <td>0.936000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>234</td>\n",
       "      <td>Stranger</td>\n",
       "      <td>nonmatching</td>\n",
       "      <td>0.979293</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>186 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Subject     Label     Matching    RT_sec\n",
       "index                                          \n",
       "0          201      Self     matching  0.710595\n",
       "1          201      Self  nonmatching  0.739987\n",
       "2          201    Friend     matching  0.789074\n",
       "3          201    Friend  nonmatching  0.852600\n",
       "4          201  Stranger     matching  0.913667\n",
       "...        ...       ...          ...       ...\n",
       "181        234      Self  nonmatching  0.874204\n",
       "182        234    Friend     matching  0.963889\n",
       "183        234    Friend  nonmatching  1.094103\n",
       "184        234  Stranger     matching  0.936000\n",
       "185        234  Stranger  nonmatching  0.979293\n",
       "\n",
       "[186 rows x 4 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "try:\n",
    "  df_raw = pd.read_csv('/home/mw/input/bayes3797/Kolvoort_2020_HBM_Exp1_Clean.csv')\n",
    "except:\n",
    "  df_raw = pd.read_csv('/data/Kolvoort_2020_HBM_Exp1_Clean.csv')\n",
    "\n",
    "df = df_raw.groupby(['Subject','Label', 'Matching'], as_index=False)['RT_sec'].mean()\n",
    "\n",
    "# 将 Label 列的数字编码转为文字标签\n",
    "df['Label'] = df['Label'].replace({1: 'Self', 2: 'Friend', 3: 'Stranger'})\n",
    "\n",
    "df['Matching'] = df['Matching'].replace({'Matching': 'matching', 'Nonmatching': 'nonmatching'})\n",
    "\n",
    "# 设置索引\n",
    "df[\"index\"] = range(len(df))\n",
    "df = df.set_index(\"index\")\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label列共有 ['Self' 'Friend' 'Stranger'] 类\n"
     ]
    }
   ],
   "source": [
    "print(f\"Label列共有 {df['Label'].unique()} 类\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过查看数据可知，在自我匹配任务中，被试学习几何图形和身份标签的关系应为，例如，三角形代表自我（Self）；圆形代表朋友（Friend），正方形代表陌生人（Stranger），随后判断所呈现的几何图形和文字标签是否与之前学习的关系相匹配。   \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/snajcrx0jy.png?imageView2/0/w/640/h/960)\n",
    "\n",
    "> Sui, J., He, X., & Humphreys, G. W. (2012). Perceptual effects of social salience: Evidence from self-prioritization effects on perceptual matching. Journal of Experimental Psychology: Human Perception and Performance, 38(5), 1105–1117. https://doi.org/10.1037/a0029792  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "因此，真实的实验情境是一个2*3的被试内实验设计的数据。其中，标签（自我相关性）是可以有三个水平的：自我、朋友和陌生人。\n",
    "\n",
    "\n",
    "如果我们对标签的效应感兴趣，那我们可能就要回答这个问题：**“三种Label条件下的反应时差异是怎么样的？”，即如何构建“Label”变量编码为3个水平的线性模型？**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "同时，该实验设计还有另一个自变量，即匹配水平(“Matching”)，包括“匹配”和“不匹配”两个水平。这个自变量会对反应时间产生影响吗？\n",
    "\n",
    "这是第二个研究问题：**“匹配水平(“matching”)是否会影响反应时间？**”。\n",
    "\n",
    "通常，我们也可能想知道第三个问题：两个自变量之间是否有交互作用？在不同的匹配水平(“matching”)下，标签“Label”的效应是否会发生变化？。\n",
    "\n",
    "Q：传统的心理统计学中，我们使用什么统计检验来回答上述的问题？\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "本节课我们将展示如何在贝叶斯统计框架下，通过3个线性回归模型来回答以上问题：\n",
    "\n",
    "- 三水平的简单线性回归模型\n",
    "- 2 X 3的多元线性回归模型（无交互）\n",
    "- 2 X 3的多元线性回归模型（有交互）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注：为了简化研究问题，本节课使用的是多个被试的数据。“Subject” 为被试编号，代表不同被试。\n",
    "\n",
    "此外，数据中的因变量不是单个试次下被试的反应时和正确性，而是在不同条件下的平均反应时和正确率。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型一：三水平的简单线性回归模型\n",
    "\n",
    "在前面两次课时中，我们使用了二分类编码（例如Self = 0, Other = 1）来表示“Label”条件，但这次我们考虑的是三水平的单因素“label”条件（Self、Friend、Stranger）。\n",
    "\n",
    "为了能对离散的多分类变量建立回归模型，我们需要使用**哑变量编码(dummy coding)**来处理这类多水平的自变量。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 哑变量编码规则\n",
    "\n",
    "对于三水平分类变量 “Label” (Self, Friend, Stranger)，我们可以使用 Treatment Coding 编码，以第一个水平 \"Self\" 作为基准（baseline）。\n",
    "\n",
    "那么，什么是treatment编码？🤔\n",
    "\n",
    "在回归分析中，自变量可以是数值型的（如身高、体重）或分类型的（如性别、实验组别）。对于分类变量（如 Label：Self、Friend、Stranger），因为它们是文本或类别，无法直接输入到回归模型中，因此需要将它们转换为数值形式。\n",
    "\n",
    "treatment编码是将分类变量转化为数值型变量的一种常见方式，通常是：\n",
    "1. 选择一个基线水平（Baseline level）：通常是分类变量的第一个水平；\n",
    "2. 创建哑变量：通过 n-1 个对比列，表示其他水平相对于基准水平的差异。\n",
    "\n",
    "那么，当我们选择“self”作为基线水平，编码矩阵应该如下：\n",
    "\n",
    "| Label     | 截距(baseline) | 对比列 1 (Friend vs Self)      | 对比列 2 (Stranger vs Self)      |\n",
    "| --------- | ------------ | --------------------------- | ----------------------------- |\n",
    "| Self      | 1            | 0                           | 0                             |\n",
    "| Friend    | 1            | 1                           | 0                             |\n",
    "| Stranger  | 1            | 0                           | 1                             |\n",
    "\n",
    "- 截距(baseline)，对应 Self，即当所有对比列值为 0 时，截距 $\\beta_0$ 对应 Self 条件下平均反应时的估算。\n",
    "- Friend：在第一列中为 1，表示其相对于 Self 的差异。\n",
    "- Stranger：在第二列中为 1，表示其相对于 Self 的差异。\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**其他编码模式**\n",
    "\n",
    "treatment coding这种以 [0, 1] 的编码方式是R语言中的默认方式，也称为哑变量编码（dummy coding）。这种方式以 [0, 1] 为编码规则，默认将第一个因子水平作为参考类别（reference level），其他水平与其进行比较。\n",
    "\n",
    "此外无序因子常用的还有sum coding，采用的是[1, -1]的编码方式，以使因子效应在模型中进行加权平均。\n",
    "\n",
    "\n",
    "其他的编码方式还有很多，如果感兴趣，可以通过以下参考资料自行了解。\n",
    "\n",
    "| 编码方式                | 编码规则                                                              |\n",
    "|-------------------------|-----------------------------------------------------------------------|\n",
    "| **Treatment Coding**    | 参考水平编码为 0，其余水平编码为 1                                   |\n",
    "| **Sum Coding**          | 一个水平编码为 -1，其余水平编码为 1，所有系数和为 0                  |\n",
    "| **Helmert Coding**      | 每个水平与之后所有水平的平均值比较                                   |\n",
    "| **Orthogonal Polynomial Coding** | 使用正交多项式编码函数（线性、二次、三次趋势）               |\n",
    "| **Backward Difference Coding**   | 每个水平与前一个水平比较                                      |\n",
    "| **Custom Coding**       | 用户自定义编码规则                                                  |\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "> 参考资料：\n",
    "> 1. [Chapter 10 Contrasts | Analysing Data using Linear Models](https://bookdown.org/pingapang9/linear_models_bookdown/contrasts.html)\n",
    "> 2. [Patsy: Contrast Coding Systems for categorical variables - statsmodels 0.15.0 (+522)](https://www.statsmodels.org/devel/contrasts.html)\n",
    "> 3. [Coding for Categorical Variables in Regression Models | R Learning Modules](https://stats.oarc.ucla.edu/r/modules/coding-for-categorical-variables-in-regression-models/#:~:text=%E2%80%9CDummy%E2%80%9D%20or%20%E2%80%9Ctreatment%E2%80%9D%20coding%20basically%20consists%20of%20creating,variable%20is%20contrasted%20to%20a%20specified%20reference%20level.)\n",
    "> 4. Schad, D. J., Vasishth, S., Hohenstein, S., & Kliegl, R. (2020). How to capitalize on a priori contrasts in linear (mixed) models: A tutorial.Journal of Memory and Language,110, 104038.\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 为什么需要哑变量编码？\n",
    "\n",
    "在三水平简单线性回归模型中，因变量（Y：RT_sec）和分类自变量X（Label：Self, Friend, Stranger）的关系可以表示为：\n",
    "\n",
    "$$\n",
    "Y = \\beta_0 + \\beta_1 \\cdot X_1 + \\beta_2 \\cdot X_2 + \\epsilon_i\n",
    "$$\n",
    "\n",
    "其中：\n",
    "\n",
    "- $\\beta_0$：基准水平 Self 的均值。\n",
    "- $\\beta_1$：Friend 相对于 Self 的均值差异。\n",
    "- $\\beta_2$：Stranger 相对于 Self 的均值差异。\n",
    "- $X_1, X_2$：对比列变量（Friend vs Self 和 Stranger vs Self）。\n",
    "\n",
    "通过 Treatment 编码：\n",
    "\n",
    "- $\\beta_0$：直接表示基准组（Self）的均值。\n",
    "- $\\beta_1$ 和 $\\beta_2$：表示其他水平相对于基准组的差异。\n",
    "  \n",
    "🤓可以发现，$\\beta_1$ 和 $\\beta_2$ 分别对应我们关心的两种研究问题：自我条件下的反应时是否快于朋友条件? 以及自我条件下的反应时是否快于陌生人条件？\n",
    "\n",
    "我们可以通过上节课学习的后验推断方法来对两种假设进行检验。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型拟合和推断\n",
    "\n",
    "在了解哑变量之后，我们就可以开始进行模型拟合和推断了。\n",
    "\n",
    "为了演示简便，我们使用一个简化的 workflow 流程。\n",
    "\n",
    "<p align=\"center\">\n",
    "  <img src=\"https://cdn.kesci.com/upload/sm7veon5ei.png?imageView2/0/w/720/h/960\" alt=\"Image Name\">\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**选择模型和数据处理**\n",
    "\n",
    "根据哑变量编码明确了所选择的模型为： $Y = \\beta_0 + \\beta_1 \\cdot X_1 + \\beta_2 \\cdot X_2 + \\epsilon_i$。 \n",
    "\n",
    "由于模型需要 $X_1$ 和 $X_2$ 两个变量，因此需要首先对数据进行这两个变量的编码处理。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "index\n",
       "0          Self\n",
       "1          Self\n",
       "2        Friend\n",
       "3        Friend\n",
       "4      Stranger\n",
       "         ...   \n",
       "181        Self\n",
       "182      Friend\n",
       "183      Friend\n",
       "184    Stranger\n",
       "185    Stranger\n",
       "Name: Label, Length: 186, dtype: category\n",
       "Categories (3, object): ['Self' < 'Friend' < 'Stranger']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 将 Label 列转换为有序的分类变量\n",
    "df['Label'] = pd.Categorical(df['Label'], categories=['Self', 'Friend', 'Stranger'], ordered=True)\n",
    "\n",
    "df['Label']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将分类变量转换为哑变量\n",
    "X1 = (df['Label'] == 'Friend').astype(int)\n",
    "X2 = (df['Label'] == 'Stranger').astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**先验设定**：\n",
    "\n",
    "本模型使用三个水平的哑变量编码，相比上节课的简单线性模型，产生一个额外参数 $\\beta_2$。\n",
    "\n",
    "因此，我们需要为截距（$\\beta_0$）、斜率（$\\beta_1, \\beta_2$）、以及误差项（$\\sigma$）设置先验分布。\n",
    "\n",
    "1. 截距 $\\beta_0$ ：基准水平 Self 的均值，即在 Self 条件下反应时间的平均值。\n",
    "\n",
    "$$ \\beta_0 \\sim N(5, 2^2) $$\n",
    "\n",
    "即，假设 Self 条件下的平均反应时间为 5 秒，标准差为 2，表示在 3 至 7 秒范围内有较高的概率。\n",
    "\n",
    "\n",
    "2. $\\beta_1$：Friend 相对于 Self 的均值差异；  $\\beta_2$：Stranger 相对于 Self 的均值差异。\n",
    "\n",
    "$$ \\beta_1 \\sim N(0, 1^2), \\quad \\beta_2 \\sim N(0, 1^2) $$\n",
    "\n",
    "\n",
    "- $\\beta_1$：假设 Friend 相对于 Self 的均值差异小且对称分布，可能是正值或负值。\n",
    "- $\\beta_2$：假设 Stranger 相对于 Self 的均值差异小，且对称分布，可能是正值或负值。\n",
    "  \n",
    "3. 误差项 $\\sigma$：数据围绕预测均值 $\\mu_i$ 的波动。使用指数分布 $Exp(0.3)$，与两水平时一致： $$ \\sigma \\sim Exp(0.3) $$\n",
    "\n",
    "即，假设反应时间的波动集中在小范围，允许中等程度的波动（通常在 0 到 10 秒范围）。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**完整模型设定**\n",
    "\n",
    "\n",
    "模型可表示为：\n",
    "$$ Y_i \\mid \\beta_0, \\beta_1, \\beta_2, \\sigma \\sim N(\\mu_i, \\sigma^2), \\quad \\mu_i = \\beta_0 + \\beta_1 \\cdot X_1 + \\beta_2 \\cdot X_2 $$\n",
    "\n",
    "先验分布：\n",
    "\n",
    "- $\\beta_0$： $$ \\beta_0 \\sim N(5, 2^2) $$\n",
    "- $\\beta_1$ 和 $\\beta_2$ ： $$ \\beta_1 \\sim N(0, 1^2), \\quad \\beta_2 \\sim N(0, 1^2) $$\n",
    "- $\\sigma$： $$ \\sigma \\sim Exp(0.3) $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先验设置：\n",
    "\n",
    "* > $Y_i {\\sim} N\\left(\\mu_i, \\sigma^2\\right)$  \n",
    "\n",
    "* > $\\sigma   \\sim \\text{Exp}(0.3)$  \n",
    "  \n",
    "* > $\\beta_{0}   \\sim N\\left(5, 2^2 \\right)$  \n",
    "\n",
    "* > $\\beta_1   \\sim N\\left(0, 1^2 \\right)$  \n",
    "\n",
    "* > $\\beta_2   \\sim N\\left(0, 1^2 \\right)$  \n",
    "  \n",
    "定义回归模型：\n",
    "* > $\\mu_i = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以通过 PyMC 构建该模型，并使用 MCMC 算法进行采样。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "# 建立模型\n",
    "with pm.Model() as model1:\n",
    "    # 定义先验分布参数\n",
    "    beta_0 = pm.Normal('beta_0', mu=5, sigma=2)\n",
    "    beta_1 = pm.Normal('beta_1', mu=0, sigma=1)\n",
    "    beta_2 = pm.Normal('beta_2', mu=0, sigma=1)\n",
    "    sigma = pm.Exponential('sigma', lam=0.3)\n",
    "    \n",
    "    # 线性模型表达式\n",
    "    mu = beta_0 + beta_1 * X1 + beta_2 * X2\n",
    "    \n",
    "    # 观测数据的似然函数\n",
    "    likelihood = pm.Normal('Y_obs', mu=mu, sigma=sigma, observed=df['RT_sec'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**进行后验采样**\n",
    "\n",
    "接下来我们使用`pm.sample()`进行mcmc采样  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta_0, beta_1, beta_2, sigma]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b6c3073de5e94f9d894ae653529363c3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 3 seconds.\n"
     ]
    }
   ],
   "source": [
    "with model1:\n",
    "    model1_trace = pm.sample(draws=5000,            # 使用mcmc方法进行采样，draws为采样次数\n",
    "                      tune=1000,                    # tune为调整采样策略的次数，可以决定这些结果是否要被保留\n",
    "                      chains=4,                     # 链数\n",
    "                      discard_tuned_samples=True,  # tune的结果将在采样结束后被丢弃\n",
    "                      random_seed=84735)           # 后验采样  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MCMC诊断和后验推断**\n",
    "\n",
    "我们可以使用 `az.summary` 函数来查看诊断和后验推断的摘要。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>beta_0</th>\n",
       "      <td>0.703</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.671</td>\n",
       "      <td>0.735</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10448.0</td>\n",
       "      <td>11581.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_1</th>\n",
       "      <td>0.064</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.108</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11335.0</td>\n",
       "      <td>11617.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_2</th>\n",
       "      <td>0.061</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12312.0</td>\n",
       "      <td>12968.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.133</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.120</td>\n",
       "      <td>0.147</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13834.0</td>\n",
       "      <td>13622.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "beta_0  0.703  0.017   0.671    0.735        0.0      0.0   10448.0   11581.0   \n",
       "beta_1  0.064  0.024   0.018    0.108        0.0      0.0   11335.0   11617.0   \n",
       "beta_2  0.061  0.024   0.014    0.105        0.0      0.0   12312.0   12968.0   \n",
       "sigma   0.133  0.007   0.120    0.147        0.0      0.0   13834.0   13622.0   \n",
       "\n",
       "        r_hat  \n",
       "beta_0    1.0  \n",
       "beta_1    1.0  \n",
       "beta_2    1.0  \n",
       "sigma     1.0  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(model1_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 ROPE+HDI 对参数进行检验\n",
    "\n",
    "- 可以看到，$\\beta_1$ 和 $\\beta_2$ 参数的置信区间没有包含 0，但两者均与 ROPE 重叠，表明效应不明显。 可以使用贝叶斯因子进行进一步假设检验。\n",
    "- 此外，$\\beta_1$ 的效应在均值和 HDI 范围均大于 $\\beta_2$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义 ROPE 区间，根据研究的需要指定实际等效范围\n",
    "rope_interval = [-0.05, 0.05]\n",
    "\n",
    "# 绘制后验分布，显示 HDI 和 ROPE\n",
    "az.plot_posterior(\n",
    "    model1_trace,\n",
    "    var_names=[\"beta_1\", \"beta_2\"],\n",
    "    hdi_prob=0.95,\n",
    "    rope=rope_interval,\n",
    "    figsize=(9, 3),\n",
    "    textsize=12\n",
    ")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用贝叶斯因子进行差异检验\n",
    "\n",
    "- 无论对于 $\\beta_1$ 还是 $\\beta_2$，$BF_{10}$ 都接近与1，表明两个参数都没有证据支持它们和0有区别。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [Y_obs, beta_0, beta_1, beta_2, sigma]\n",
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 进行贝叶斯因子计算，需要采样先验分布\n",
    "with model1:\n",
    "    model1_trace.extend(pm.sample_prior_predictive(5000, random_seed=84735) )\n",
    "\n",
    "fig, axes = plt.subplots(1,2, figsize=(10, 3.5))\n",
    "\n",
    "# 绘制贝叶斯因子图\n",
    "ax = axes[0]\n",
    "az.plot_bf(model1_trace, var_name=\"beta_1\", ref_val=0, ax=ax)\n",
    "# 设置 x 轴的范围\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "ax = axes[1]\n",
    "az.plot_bf(model1_trace, var_name=\"beta_2\", ref_val=0, ax=ax)\n",
    "# 设置 x 轴的范围\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "\n",
    "# 去除上框线和右框线\n",
    "sns.despine()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**后验预测**\n",
    "\n",
    "最后，我们可以使用 `pm.sample_posterior_predictive` 函数来生成后验预测。\n",
    "\n",
    "并通过 `az.plot_ppc` 函数来绘制后验预测的基本结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [Y_obs]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cafe5fa6b386420d9a19df4f867cab53",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model1:\n",
    "    model1_ppc = pm.sample_posterior_predictive(model1_trace, random_seed=84735) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Y_obs'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_ppc(model1_ppc, num_pp_samples = 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AuOqqq7Bnzx489thjbPs77rgDd999N3bv3o1kMonzzz8f3/rWt9DdXV31/OhHP8KXv/xl9PX1YdmyZfjmN7+J973vfQ2PSZToCgg0juzTB2BlDQBzM2HUmwSDyxKusPxsjzPdGN9uZb7FXSmU+iZ9P5uqHHouMbmpX5CPtynmnYQcjRAkRECgccxlGqMR4mCOF5HbMuz72aEc1ws/X4vQ8c3Qe2LTnu9ohmParILJi5kSvUNF7rlh5LZUNXyBpUlBPt5mECTEB4KECAg0hrkkIFa2jOzTgzXVbPyxM7/dD7tksVWzvjgBSfbfth6yzxyAlTFq3o9fsMh1LB5v9ujI0VhlMnLPi+zfgny8fSFIiA8ECREQmB5zXVlCQ/J0JR5d3wklHnB9DtRWS3jD+EDjeg7jYB75rbUt4SOndUJN1FbM2SUTmd8OuN6Lnt4FJaZPe64jiaORdFCM/fA1WJMl9rr9k2vmcTQC8w1BQnwgSIiAwPSY6zQMTy68x/QjIImLemEM5ZB/eZRt50dIGu0jUy9NoXWEET6xzXfMXszXBF98YwKlfn+n5/j5PZCUee9V6tJ9AEDbn504pX+TwNsDgoT4QJAQAYGpMZcEZOJ/+2Dsz0BtCUFJBBomIPXGRFHqS80qXVPvePWOYYwWkH9hxPXe4RZ0OoaF9GP7fT8LHtuEQO/R89ya3NQPK12COUr8Xd5MqRdrsoTs74cQObUTalJ4SR0OCBLiA0FCBATqg07OclBF7Oz6XhyNgNcFtH3ihJoVez0CMrmpH4ElCQSPSU45RgCAbaO0J10juDwchORwRkeO5hSLH/jvDiDkYyrdzdECv/scXtMGrT08D6N560OQEB8IEiIg4A++YuRQJ76R+14CbPL48dMFTEVAvKg3FnOsgNzz1SiFOV6AlSoddkJSeG0c5X2Zup8fynlmc6wjCebVkjdgDOWO+pLberogiqN13G8VCBLiA0FCBAT8MRdpmPK+DArbx1DaQ7wppiIganMQ5niRnZOfmGPnLkRmszslMZVI1Ddd0xt3RV+09jDCa2r1H/XQCCFplDTxvW28eLNFEHjiOBc9ZOYaUxE8CkE+jgwECfGBICECArWgD+7wCa3QOuv3aGnkGHSS8j7oaQ4eAGLnLETmt4RkxM/rYaLR0Ipm6AvdXh0zTYP4ERJvdCR2djfkYOOm0qX+NIpv1DZzi53VDTmkMkdQCsey6wpG/a7xaAV/L52yBUmvEo6jZSIv78+wPkTT4WgZ89sFgoT4QJAQAQE3eIOwQ23JTid87+re67xKt9faQzBGiKgxfuGiKSsqjJE862FDMVUUwUwVkXt22PWeHyGZ6TXbRROZxwdq3rcmilCagq4qEQCQdAVtH1s9o3PMN6aKJsQ2LIAcnr4i6XCi3vgi6zqgJHSkH3VXQgnyMT8QJMQHgoQICLhxKGmY7O8GYaXLAMiKVF8Yg9ocRGRd1cfD6zkyFwLPQ42OOJYNOKipcpmNfsRLOgDUdSY92idD733ypsXmrUx5Zwql3f7283RMdsli0TXvZzz43ywASBIQv/Do/l7erBAkxAeChAgIVMGa072jB5I2s7LTmWomeAJily3IldD+oUxsuRdGWHmo3/n94B23eTAPta22OsJ7nPzWERgHCzXbAdWIjP89cQC4ozVH2kJ9OnjH7SWLkVM7oCaD8zomiugZXVCiVW2QlSkj+8ygaxv+u+O7MfvhaCeGb2YIEuIDQUIEBAhyW4ZdwtCZgJ8g9J4YqxZphIAYgzloXZFZnbfRMQGApEqIn7eo7vbUSp4Hn65xDBvlfWkoMb2GpDSinfGbROciHTSX8CMfjmW70hlHanz5l0dhDPmLd/3G4OfhQrebTpwqiMeRgSAhPhAkRECAYDZpGP7hHjyuCYFFcd/j1CMg05mSzQVmk+7xS614xaWBpUnEzlkIOTDzahC/dFC53+1vciSjDX7kw/v+oYiUZzsOiqmEw+V9GRRecwtRo6d1MtHzVBDk48hCkBAfCBIiIHDoBMQ7aU1LQBwHpd2TCCxNHlHXT+8kFzwmicCSRN3PAX97eD/MdkLzluv6New7UgSNnsebsjhc5/fqMfzGUg+FV8dQ3p9lr8v7Mg11PT4a+/+8XSBIiA8ECRF4u2Omzekcy0H60doJih6Hjw7Q94LLkwgsTmByUz/Mg3lYmTKpmpmmAmZyUz/yL44geGwT5JB/BcZ0aZZ6xwWA8kAWTskEUEsyvGOz8wYyTx5wbeOYtq9l+2wnbStdRvZ3JCVkF00YB8gkq7aHoUT1OfPhqEc+vJ8FliYQXJY85PNNdW6KRnVIud8PwZwswTiQhV00IUd0aB3TO5yKqMf8Q5AQHwgSIvB2x0yiIPwEwgsCvUSG11fQ3ir5rSNsgm2kp0juuSFM/M8uAIAcUgGb9FEJLEkyDUmjiK7vghLXYeUMZJ+qEgmaBgEArSMCOaLVCB394DeRKjENVsaoeX+2kx8fjeDTQpKmQO+Jzfi4foLMqazo52rS9nqmTHX+qTD5636UdqXYa6UpCLWJpKto40Lv9+KtzBKYXwgS4gNBQgTezpgtAZkq3ZJ7dghmquTazsoZGPu37QAaIyDFXSmMPrANACEg+oIYygfc1uiBnjjU9rDrWJnf7oddslzb+ZXMsmPMQYqlEUdOAAj0xhE8tqmhbeudx5wowpoout6frkPtTMlHvU7CMx2rH2bqBuvtxgsAansESlRj11DcOYHSbndXYRH1ODohSIgPBAkReLuCThTTVo14Sh75BzxvGOYt4+S3o83rGiIgfSmM/eBVOKYNtSWE0IoWhI5vht4Tg10yMfq9bTC5iVhtCiKwNAFAqus7QhG/YBHrh1MPdrYMYyTvei+wJIHAsuSUqQm7ZCLz21rTMt9xHGJaxW9yBty2+I2QD3qsqT5vdDz1MJNj8r817/U1f/B4qIlqd9u5aiDIm/MBgL4gitCqlhkfR2B6CBLiA0FCBN6OaLQ5Hf+g91vF8pGUuSAgqZ/3Ib91BHbJgr4g6hup4DUopb4UjMEcHMch1RMSWIh+tm3kS3vTKL5OLNlnYjwGAPHzF0FS/P1BIqd0IPfccM37h7pqP/idl+GYNnvtOA4kSXKNczryIYdVxDY03iV5Kq+N6XQ+U40DqN5zOaJB64gwK3zA34Asdu5C5jFzKOOmmOn4BRqHICE+ECRE4O2IRtIw062QpyMgjuXg4P0vAQBi5/UgdGzzlGNK/WoP8s8PE7FhSEVkXScAoLB9DFJAgZUqQonp0HsTMAZIaiawNIlSXwp2yYKdNwBIkBQJSlxnnwNVcjBb5J4bgjlRYq/9/D3qwUVkJAmBJQlEz1zg0qZQHAohcWwHQ3//HHF/rUBtCSGwOFFDIGcT/ZiraEc9kzfvPaVaonrnnstUGQAoCR3R07oa3l5g5hAkxAeChAi83UAfzPUap5X6JlHkBIBTEZDIug5XKJtuW3htHJnNxOAq8a4l05bgph6pEJCCm4DQCZxPv9gF07WvHFKhxAKQdBmwHbatYzmMeCiJAJuEqQCV+prMFN6JTdYVxM5d6HrPK4Al46mKYL3j569J645BDigNT+x8VMs7BnO4WvpLCZu2IMo8N6Y6R73jTrefH+q6nZ7eVeNuyhMm736BJQkEj0n6Hiv/4gjrO1QP9czLhIbkyECQEB8IEiLwdoKVLiH7O2LiNFt9wHT27LxeYbqUCA2P57YMwc6UIcd0RNZ1wjEslPdlYE4UIWmKSyiZuKgX5mQJud8PsfM4ZRtWjvhNKIkArEkStaCkRkkGYFXEsjRdAwCSIkOfpUcJH+GQwxq0zsiMogrlfRk4RlVEq3VGfB1C1eYgFI9pWeKiXl+SUO87dWwH+RcIWZQDKkKrWyvnDCN8QptrWz9IsoT4BY2XQTcSNalHBLxRJ/4zinpNA6faByAl1bRDM78N33lX0mTE39Ez5bEFZgdBQnwgSIjA2wlTpWFmS0B4L4mZEBC6cs1tGWJkIbymHZIqo9SXgjlRrIhOp9d20MiDXTBhDGZrPncsG1a6TBxIJbiOzSNxUa+vH8hUcBwHZU8zNbUlBIUTUU4FP91J2zUnYvLX/TXHDSxOwAFQ3uN533Md3u+EPw+NiADEEI0/1nQ6knrws7yvd5xG3Fkb+YxHI861rgqg1hCgyr6kT0RFDh8ECfGBICECbxcwMzGPkC/z+H7YRbIiV1uCiKz191Wgk7NjWKyyg6/ymAkBoWPJPEFEhnJQRfC4ZigxHbktJFKjNgURv2ARgsfMrKzVb8Ky8wabcMyJIiRFZroRc6IIOaJD1mU2dmB2k1HNuW0HaLAk1bGdGnJBx1PqS8FxHBbNAcj9UVtCMMfqpyDMiSJLRdHrKu1KwUwVoSSDkCqETInqkCOaKz0308Z/bFx1fkN+5IM3Z6Ogwtp60DojCJ/QOuXY6p231DdZqaSqhSAfhx+ChPhAkBCBtwP4ZmBTeXxMhclN/TCGcqx/iPc4h0JAIie3A4rsIiC03PRQ8vc1lRd7JhFYXJ2Eiq+Pu1w6aYTEi5lW2viV61JDrUaQ/nU/2NPadlDaMwm1LQxrvAhjNF8zRm8khI+uGOOFhqs9aESKQILaFGDHNw7mCVkJ1fZwaVTgTLel71mTJUai6gl9Z0sO7LKFzOb9vrb7xmCW6XACSxMo9bmjQYKQHB7MOwm58847ccstt2BwcBCrVq3C7bffjrPPPtt326uuugrf//73a95fuXIltm3bxl7ffvvtuOuuu7B37160trbi/e9/PzZu3IhgsLHGT4KECLwd0EhPl+n292s2R3UJVrYMp2RBbQlNOyEZg1kmfJUDKtSWIPTeOIqvT0AOkqhKPQIyFZSIhuiZC3w/M4ZyyL88yl47pg1zJA9tQZRdB189YucNlHalIPuQBr037mpkN5uIQUP2+IaF9GP7XYSCv//ZZw74OrQC9fvd8EZkxV0plPom4RgWSrsnYWU8PVwcor3wggiBdUiqDK07Cjng31jOm2bSFyeYLoUcR4PeG3cRs7mY/O2CiaFvb6meR1dqvkc7b0IO+4+b91oRmFvMKwl56KGHcOWVV+LOO+/Ehg0bcM899+D+++/H9u3bsWhRreBpcnIShUI1zGiaJtasWYNrr70WN910EwDgBz/4Aa6++mr8y7/8C84880y88cYbuOqqq3DFFVfgtttua2hcgoQIvNXhJSD8pBha3Qp9Ggt0SkCoTTZzqtwxgdKeNAmfA4Ak1Z1EqGaj1JeCMZKHY9rQWkOQKmkhxwEkCdAXxZF89xLXOP2st/2qT6aCviCC0KrWmusHaktDlbhe01RNSeiwJsuwcwYMruJkKu2H916UD2RR2Dbmes/Pe4Wu4L3H8vbs4T+b+N8+FLeNwbGr5bnBY5qgJAIzjhz5aVT4SiMe+qI4JFWuSXcB1Somv8iJ2hR0VenMBH7joxVGpsdNlo8YmRNF6Ivi0NrCvscR5OPwY15JyPr167F27Vrcdddd7L0VK1bgsssuw8aNG6fd/yc/+Qne9773Yffu3ejtJX9Uf/EXf4FXX30Vv/nNb9h2f/mXf4nf//73ePzxxxsalyAhAm9l+Haw5V43sr9fmmUmq/vJTf2wMmXSuC5VgpU3oER1psmg8Dt+eX8GTpnoVfQlCURObJu2nbzXAXMqlPpSjEh4owd+ZAQAYuf3IPPoPtd7dq4MYzjfkHdIPVfX2DkLa4y46t3TzBMDKGyrRnbMiSLksAY5oEBJBqE2uyPB9XxSphLhBo5JoLTTrVGJX7gITsmqqUwp9aVgHMz7NvMDAEmSoCSDvnqMwJI40/0Ud6VQfGMC5b21pcx+YKTDARxUtSRqUxCOA1gp8rkSD7Drn4qoAOR3lrx4cUPnF5gZ5o2ElMtlhMNhPPzww7j88svZ+9dddx22bt2KzZs3T3uMSy65BKVSCY888gh774c//CE+9alP4ZFHHsFpp52Gvr4+vOc978FHP/pRXH/99b7HKZVKKJWq4q50Oo2enh5BQgTekqCTXfy8Ht/SxKmQfeYAs2SfjoDUc5nkSYyVLsMxbTglC0pzEHJAYaJLv+NP1fNFXxRH4sLehrqu8ijvy6Dw2njN+8ZwDnaOpDbMVAlwHMhhDYHeOOSwVpc4TGUTn7iotyYNVDOegQzsgglrsjSt06sfuTJGcijvy7j2pecGZpbOUpMBRE7t9P2MPw6tQKLnojoeoBox4SuP6FhK/ZOY/OWehsfDI37+IgSXN9WMBfBU/eyccAmBA0sSKO2ehBzRCKE1HVYWrVdScTwkRUZkfdeMhK8CjWPeSMiBAwfQ3d2NJ598EmeeeSZ7/+/+7u/w/e9/H6+//vqU+w8ODqKnpwcPPvggPvCBD7g+u+OOO/CXf/mXcBwHpmniz//8z3HnnXfWPdZNN92Er33tazXvCxIi8FaD72qbs8CeCo7t4OB9xO10OgISPa3TNyWR+nkfyvuIs6mVNeAYFhM+estjaZdbPwJCz+8VGlJonRE0XXrMtNc0HQrbx1AeyFa9R2yH+Y3wk7yVLsEcLUDvibn6v0xHSHiUD2SRf/Gga8XvFcVKmgzHsH2jK6EVzczXgh6/nrmY3h1FsS8FY6C2dLmRFAR/TeWBDJxKg0AaUYis7UCpUkrs7elD0WijwHr3z4+QWpMlKIkAzIkinIIFbUE1QhZYmkT8wkVI/3ov8i8ddPmxhE/ugGNYrvtxKBVRAo1j3knIU089hTPOOIO9/81vfhP/+q//itdee23K/Tdu3Ii///u/x4EDB6Dr1RDuY489hg9+8IP4xje+gfXr12Pnzp247rrrcM011+ArX/mK77FEJETg7QB+Mp/NA5b2e4m9oweh45pdx+ShxHVE19daXdP9AdIDxBjMwcqWfQmIHFIRO6vbNWZJU+AYVt2ogOM4mPzlnpqwvRIPoOVDxzd8nVOB12Dkt44wO3S1KUgqbGTJd3LUe+KIX7ioRtdBEduwoCYFQq8x/9JBpH7eV7MPf8+siSLMieKU3+vB722DU3KLSpWmIBIXL0bh5VFfwelUJIpqPviSYHO8yCz2KcIntDGdD/Mi8SFrjcBvLFpHGOV9GeRfPgjHduCUrOr5HbjSUOZoAXa5Sj6CK1pgT1af/XzTQ4EjgzdlOsZxHBx77LF473vfWyM2Pfvss3H66afjlltuYe/927/9G/7sz/4M2WwWsjx9qFZoQgTeanAcB6mf9cE4kJ0xAbGLJka/T6rPWj6yCkpIda2w9QVRlA9UV5De4xZ3TLCJW1sYI1UmOyZg54yKG2oHtI4IjOG86xg8AaEGWjMplRx/+HWY4+5cP2QJ7dec2ND+08EvQqMvjEFtDTHdyFTN7szxIsyxAqx0iRmmAUDrlSvrajJCJ7ai8BJJ5dBSVrtkMVMuOol6z92oLiX/4giyzwzW+I9QbYnrWI5TE+1Qm4KQgyrsoulr+sajkQhRPeFt+MTWintuCaW+FKxMmTXskwMq5LDqOn9+6wisbBmSIsOxbEiyBKlyPZKuQIloCCxJECX0FOMRmHvMXIY8R9B1HevWrcOmTZtcJGTTpk249NJLp9x38+bN2LlzJ66++uqaz/L5fA3RUBQFjuNAWKIIvF1x8N5qGsWv+qIeCq+MIvMkERyGVrdCCamuPjLx8xe5JgnvA5uPfiTfsxTZ3w+htDPFEZBOX3GsN2rDa0QyTwzU9IrxO3/zHx9XOw7bcY3pUKofquci4y3tnkR5fwbl/dVGevT4fOVOqS9VdWutVBdZeZNFKYb+8Xl2DjmgouNza13aGv0ikmIY/68dlW3IZKovigOQXD4bFF6zr/JAFnbBACQwssHrOOi4/BA7p5v4nXDHo3191NYQ8XfhQL9L+n9alcR/V4VXRlEeJJU0qV/sZtEsfXGC/Vb5Bn/5l0ZR6ksx8kujaXJIhdbl1nXQ+w0Aki5DayKVMIGlSURO64SaCEzZE2dyUz+01hDCnusSmBscFSW6d999N8444wzce++9uO+++7Bt2zb09vbihhtuwMDAAB544AHXfldeeSV27NiBZ555puaYN910E/7hH/4B9957L0vH/Pmf/znWrVuHhx56qKFxiUiIwFsJdNJVm4OuiXk6+FXBzKSyxjvZj//oDRR3TMDOlmdFQOIXLIIxnEfhlVHf89cDTe34jYttE9XR+uEV0x5rOlg5A5nf7q9JCTEyki5h7N9JqpmPHmjtYchRnTWTMw7UajWAahTCG32hxAcg0QM5oFRISRWF7aN1yRsASKoMOahC0mR2nsCiGILHNZNU1y/2oLwvDTtvwq4QJko+Ztu9lu7HC2ztksm0GXpvnDX4U1tDMEcLcCwHxnCOpVzUpiC07hiip3VCaw+zc1HrfwCulN907qqz9XARmB2OCrOym2++GYODg1i9ejVuu+02nHPOOQCIOdmePXvw2GOPse0nJyfR1dWFb3/727jmmmtqjmeaJtOVDAwMoK2tDZdccgm++c1vIplMNjQmQUIE3goo7pggpY2VCWomq/7JTf0wJ4qwKjoDP7JQ2DbGVqL1nFLloIrWj67C8D+/AGMkD5g29J44Wv5kBZS4DmMkz6ptpiIgWmsIwVUtTFMx1aRQHsiisH2s7ucU8Xf04OC/vFzzvtYdRdN7l027/3Tg74Nj2jDHi1BbQ2xlz/drmao/C39PrEwZFhV6qrJLe6E2BV1+HPwkTUHPw0/E3g7J9FwUjmHDypbZsRzDZhVIs+kr41g20o/uY78vgOg65AjR9klBBU7RQmnPJIkYVSI1clBl1yfJEkKrWtH8/mNdxz74nZdR4gigHFIRXJaEkgxOOz4v+ajXUVpgbjHvJORohCAhAm92eCfz2dia8/t6CYhdMJF5YoC9pkj9cjdbuUbXdyF8UjuG73yB6D1MG/qiONo+vpqITCvdcukx6hEQ7+ezXZVOFzXh7eEpAksSSByCP8TEf++CMZh1aWbkkAq1NYT2T1S1KTQdYI4XmY8F4CYq5kSxurIPVhxKNRl20YRdMKEkAyzlYpcs2PmqcyqJAlT1Ig2VY/9uELnnh10N3eSQCiURYB4epd2TgONMq/+gyG0Zdul0eLLDR4b46yf7DblIFo3AAAAcB4XtY64qHDmkskjbdKhp5lcRGPPQ2kIInyTSMYcDgoT4QJAQgTczvJN57Ozuhl0oGyEg/Hb8a35CafuzE+EUTIzc/zLRJ1QISNPly10hc3oM73nL+zNsFeolIDM1V5sKfu3fHcdBYesIHLv6aFSiOoLHNU97PjrJ+nXubbv6BIzc/SKLKlDo3TGX2Vr+xREmsiQDAiBViAQnnqznmdL2ZycyMuJYDg7e/1LNNlMJVQNLE0j/miNssoTA4gT07ijKA1mY44VqdCKqs+/TbzxNly9nkS4e3vvjWA6sdLX0WeuOVSqGBlxls3w0b/jOrcSplrtXckzHguvX+15X5skB2PlqOso73qnuiUjHHD4IEuIDQUIE3oxI/2Yvmzj5viczLX+kRCB6ZheyT5Fupnz4fioCwhOX7HODcCqdeKMbuqE1BZnxFTNMq/g28Of1jp11+n3HQmQeqy1xlWQJ8Qtq2zwcCug57aKJ0q5UTfmq2hRkLpr8feNTF95OtTwc00b+xZHKC1RJhmfb7HODjFBQh099SYK9Fzm1E2oygPL+jMsjhIL3a8k+OQCLm4Qdy3b1uzGGcigPVLUlkipDXxRnkQneuMy3VLYnCmMfIQy8yBWotWvnox1qS8iVVhl78FXipstFNlo/sgr6gihSj+xBefekOyqkK1BbQ1Cag7A81VA1956r6KHwpin5a4ue0QUl6nbxFZhbCBLiA0FCBN5sqCfunCkBMQ/mSWfWiukTQJxVqfU2Iw/vWIjcCyOwJsvTEpDYWQtdY6HHCJ/cjvwLZCKmBISWd3qvwy6ZrCmarCuInbvQ97oPF4yDeUz+ag/K/enKapp7bKoy8zCRQyokTYES1dgE6BeJcreST1UmVQuSDKgdYcCBq4IpsDSJcn8aeq/7eeTrl2LYSD+2r+Z9vsKDP3/+pYOA7TDLfCURQPK9S5F9erChe1PqS0FJBJiJGw9zogjHsN2RHUlCbEN3zbZ8Gg4gRI0SofyLI7AtGyjbgO0AtgM5qkNtDtY0D+Rt/QFy7+xcGVJYc1UIee9dac8kijtSNZ8XXhtH8LimhrsOC8wMgoT4QJAQgTcLeF0FMHMCwreXpw/9emZm9LjBZQkUd5HVJL9t7JxujD34GspDWThFC5IkIVqZbKZyv6THCCyKobSXrMTjFyxC+jd7yQQX06FWGoz5XZNfW/iZwHsP/eAN3ZsTRcJDZMApVydZJawheHwz5LBWs72aDLBUil00WQUMX/FiZQ2WllCiOoLHNiGyrsMlkPRregdM3aen3jW5dBRhDaEVLdPeP2O04CKPTtmClTOqZMO0gQpplWQJwVUtUBNBhE9qQ35rNTVjjORhc6kpu2zBHC1A1hVAkaqVPI4DWA6536oMSBXB6fImKPGAiyR7Mf6TnTC55oIAud9eR1/+HmkdYZdnDVCtEhKYewgS4gNBQgTeDOAfnOGT2qC1hWcUGSi8Ns4s1CPrOpDbMjwtAbHSJSjxAKx0GeYoac7G72umS4DpAFJt+eZUBCS8po1pB9TmIEp7JmGOEq8LP2FtvWNRtH38BFbBkf39IKzJ2qZzU6Fe23t6PeXBHCsVLvWliJCR05CozUEUd6WYcRY/2StR3dXfhpYfAySlRsWePOoZzPna8G9YUEOCKFI/24X8K+6+NaEVLUhesqzGJyO0sgV6d20vFW+JMy8otYsmq2KRIxohFBXoSxIoc+ZmdsEkHicyIRw0CiZJEvF0qpAPOVZNh0iqTKI2FQJRT3TtvS+BJXEEFidcvZIAUkklydV0kd/3HX/HQpe7q8DcQpAQHwgSInC0ox7ZaDQK4pe+mY6AuKpWKgLJxEW9LE9vF0yWSpkJAYmd1c0qbej7FM1/fFxN99eRe16ENVmCFFAhaRIz/QKm74bKQ+uKMo2C4zhsgvQi/q7FCPaSTq/e8l/eg4TeQ16vAJBKFrU5CMgS9AVR2EUTStzdV4e/ZrUlhMQ7F0PSZCKa5XQMjZTy8qgnHAaIv4ikTze5Oij11d4Xep/1hTFoHVN3MKbntXMG7LLlKh+2C2YlylGZhlS58m8J0dO7GEkOLE3CGM5D6wjXHNcP1ejcQmbmxoP6iFD4VeQIPciRgSAhPhAkROBoBW3YRnEkCIhTtlDen6kpm42/YyEO/ssrAIgOwXFI+3ovAcn8dj/sUjVHTye2wNIk4ucvQn7LMMzJUs2k4udrMnLPizCGciTn7/HJ4KE2hViLeP56iq+Ps5RPI5MYBW1QRyHpCrSuCArbxlyN0CiUZMBle14dV9BF4GgqaKrIi99YXU6insnSzhvIPHmAESuXKVpnBIl3L3FFKAAg+/QBWFnDVflijhXhSBWnVZuk7tREAHLEHWWZzhJeDquInNqJ1H/vYk6uNO1E7dMlRYZtWtUSYx+TMR58Cmb0X7e7BLWAp4QX7siW917GL+hF+jd8OibCrlFUxRx+CBLiA0FCBI5G8OTBu8JrNA3j3Y5GMbSOMAKLEy4vhPRv9qK4cwIAeXg7huUKS9OHOXX4tLIGQie0QpKqDcDMVAm5Z7lKCdtBiesBw3fmpagXYh+550XmREodVwESxYBps1Uzhbd7K6kqAViTFg7xCxf5Cg9L/WkU3yD3wDFtFF4ZZQJOvqOuJEtQEgH/ShjLQbnf3WPFi0BvAmpryLNjbSUHvz9NYQSWJqA2k3295c48AaHEJbSqhbWs538PjuOg+OoY6W5ctpi2g3bulXQFkiKxdFIjRmWlvhTTD/EVQXxlS3htO8p7M650TWBJAqXdkzWkwX1//aM09DhWtkx0JA6YbTsfhVEiGqycwe6PkgxAbQ75ktPQiW2InbHA9xoFDg2ChPhAkBCBow3TkYxGoiDeY4z/eAfMg0SAx2soAMAYzmPiJ6Q3Cb/qloMKzHQZBu2PsjhBnC0NG4Fjm1wExHtOp2ShPJCpEhDDdjmW0tJTvzRDbssQ7EwZUGTIAQWvxYdhDRWwZhGxWte6omj6w6rLqTlZQnpTP4o7J9ypEa5ElJ/Qwie3Q+NIQKkvhclN/SzFJKkylJg7NN961WrfUP9UoFoSL0Eg6YYc7JwxbWTBGM7BGMhWe2HZjjvSRBu5xQNQkwF2X0u7UjDHC65t+WokSZNJlYlU1a3QRnaU8NG+NJIis0odPwLHf++FV8dcxmn0mls/thqZzftRfGMCxggRj9Lvh49kWNkyzJGqUJSWQfPmZTyhAOD+zgMqqa6qRFWsyZLLA4Z+t1aqVNNfjKZpEu9agkCvmAsOBwQJ8YEgIQJHC/hKBGDuCMhUTdxodAQgRlq022js3IUY/e4rbLvWq1dj9DuvwHHIylWS6xMQms7gy3jpilNtD7N0gvcaxn+yE+W9aVLhoMpwmjUs+py/GVWjGLrzhboN/OyC6Yo2SIpEwvNRHYmLe6G1hX33axT8PaHl0ED9jrfTpQNKeyYx+as9AEjVDKtMcUCEso7DKlXYNekynLxZ3c4i+2idkZqyYIBESIwDOTglsyYSQ+FNi9kFk5QZV9I+jmExbYy+KM4iWi5RK9cNuHpgYpQGkNJbg1a6OKTCSA4R59jgsdXKFbUpgMgpneReOw5yzw+zfSCRKiBJIn1+eC2IlTVcqTWeqPo15hOYGwgS4gNBQgSOBvATVr10Ad0m0BtH8NimKY+jtYcRXtPmslb3M2qqp0+g7+uL4ki+ewkjMnpvApLiT0Ac24E5koedd6/w6bFCK1rYytyvAZ41WSIi1JCKhV850/f6jgSu+8An8bVP3OB6b6Z6gamiWfxn5b1pUi6tK67S3HoiU3OiSDQbuUoFEE86KMmQJUCWIIdUF3mQZAmO7RAb+LhOmtiFNGhdbrGpMZSriWZQAuEULTJ522ATPXSZnV8OqVCSAWidERbRMCdKABxGAngDNsDPzl2CnNAhyxLkiA6tI+xL3CKndkBNBl331LEd5F8Yhh9oNIW3vJfDWs218i60AnMLQUJ8IEiIwHyjEY0HFSDW28YxLKQrDqO0bJOfwHgCwusI5LAGtSPMHrrGwTxJhaCq12AEZFEckirXKeclZbwAoHCt4Zm41XGYbwa/Pz22OVEkxmAS0PO3Z019w45S9Pf3I/E6ESYYgznYRYsIU6cAX7VBvTdkXYEjgxnAyQGVkI5K+kRSZWafbk4UoUR1OIZNut1WogYUckiFU7IhBeSqG2pzCOZ4AV60XXNi3agRQL4rO2/C5PrdSJJExhRQoHVFobaGmBDWmizBGMlDUsgx9Z5Y3fJXeh+YfqRSzgvUF54CgDFegFO0GOHyNvlTW0OQNAXl/RnYmTIcxyHVSpIEK1Ws3ivO70RtDqHzurV174PA7CFIiA8ECRGYL/CdaSUJiF84fYrFj4AUd0ygtCft+pwnIPzKzluCyx7cHmEkJS2MgCyMQtJVX0fVen055JACu+CuJvEbnzFegCQR/4h6BGT7ccezf//Tqg2488ff8d3uzYjhu7cC4JrWmQ6ksMqcQPmJNbymHcl3LwEAZJ86ACtnwC6aKGyr+oH4laBS0PvvmDbz0fATZ9L97IIBYzBXI/wNLE0idHwz0o/tQ3kg43ZKdQAppECrCGh5UkpBoy1+Zdb64gRJlXmMx8yJIiRFdglPYdokKgMQ0iIBclRj43BZ8FOiYdpMxEr2Q/UYEhA4rhltH11Vc08EDh2ChPhAkBCB+cBMjMbottEzF0DxlEzWazhX6ktBCqiIntaJ0MqWGutwrSsK82Ae+qI46d1REa3qPTEk/2ApgCoBUTvCUCI6ImvbobaEXOflu77yeXXqgsqjWs1RrXSg1Rn3bX4QN/3qH32vnycgruNd9T0AqDZw4x5vkkyIkmPb7LOFf32G73HejPjaO6/D1Wd/kEUZWJSjMwJzqNY1dCqiQWFlyyjtSMEuW3BKhAwBIJM0SJWSl0w4hg1IEiRVgm1YMAdzrhSR2hqC3hWFHFZdFU1+7q08zFSR9YYxJ4pwLIeRMkmTAUVi37tXY2JlDTglk7zHiZPN8SIgka7DKFouN345oTOPmpYrV0KpYwAncGgQJMQHgoQIHGnMhIAUd6XYhD2VtiBxUS+MoRzyL5NqDNpjw9uJFqjvo8BXBTAC0hyEkgy62pvXKwvly22956Q23kxrsjiB0s4JGCP5KdMv9QgIReyK+1k5KUB8KhzDgWNYlTb0SQSWJBE8JgkAyL0wgtzvq31S9EXkeo3BLJlQ4bZW37b3NZz/dx+ccgxvJrxx11NISG7BrdoahhxRUe5PV9InMkntgERhAksSsFIl6D0xRiT4qhWAEAWtLczup+M4yD/v1mYQ992Sm6ye14PJX/cz3VI90O1zW4ZYykbSFMB2EF7bDjmguggxAEggbqx2tkxCjYpPqolLw9CKmtg7ehAStu2HBYKE+ECQEIEjBX5inkpc6rfPdASEvjaGcqxVvBJWXZ1UAZ6AJFy+C7xmhBIQOaIxh0x6/tzzwzDHiijunGC+GWpT0FdzQjvkWpkylJhe7Q3TGkJp9yTKB7J1Ccjzy49FUPbvEcIjcdX3mODQKVtwrMojziGVIWprGJJUu+q38wYxQnOIfqOeERoFHwEwhnIkJcCJF+n+cliDHFDwZ/d/CT997lfTjv/NgO7WLrz0z//H7rGVMxBZ1wkrU0bxjXEXEeHvExHROnBMh6VQKPw67FJoC2OQdQV6dxShlSRCMvE/u1wpJ94O35XSkSRSXi0RTYpdMEkjPHZiQAqocCybNCCseL6wc3dEoHdHWQdhgbmFICE+ECRE4EhgNh1gWRdbT7VMPQLCiz95eMtkKTkAAL07iuR7q54brJxXkVlUhI7XyhnIPnUAuS3DoLFsvTuG1itX1oytPJCFUzKJx8SiGDOjMieKKO9NI3dwEstvvsj3uqeLfnjResOPYOeIK6ccJP1baKidt1VXIhrCJ3e49uUjQdqCKOuAa+eNuj1ZqKBX64y47n/5QBbGYNa1rRzRIesyHNuBnTWY+VlgaRLxd/S4OuBmdxzEws+cOqNrP5rx3Y/cggsXcykwyyHRiEr0QQ6p0HviTGTrF7UD3OJdJa4juLyZVOU45LuguioA1QohRSLnU2XmHQLAdW6AkCApqDJDNzoOgcMDQUJ8IEiIwOGEX+fbRjBdvxj6vvehbaaKrGyRblPYMYHMo2QM/Gq19WOrXZbelIDYZQuh41tqzj1yz4uw0mW2qo2s6/QdW27LkK840i5ZKLxyEN03nF73umdKQACg5fM/BED6sPCrWitdgnGwQKogXIZWCuSQhtDqViQu6nVVHnmvmcfIvS+5ms2pbWGmpQEArTMCOaxVo00VczcrZzA9gxLVETyu2ZU64Ks66H1rtJEfADzys1/gA//45/Vv0JsMe+/4PeLHtaOwfRSQJKb1SL53GTJPHUBpx7jbhC2kVrQplYoiB4AqEe8UWYIS1mAXTEhBxaUN8f5GD1z7rpqxrHjt1cN+vW8nCBLiA0FCBA4X+Ekjsq6jpjlbI/v6TfJqSxCRtR2+Wo/A4gQgSyx6kv3dIPJbiQEaHwHxeoZQAmJlDYRPbHOdu/DaODKb9zGDJ6/+AyBpmtyzQy6Sw6dAHMdB7vdDWPgVf3HoV959LT51zocx+b2rGr5HFB3f/G8WYaDwqzYq7Z7E+I93MJMqfhLSe+NMlxBYmqzpKuvnqcJbtPPvA6ghIkpzEEoiQPq7jBZgly3Adgj5kCUAEtQmfyt4YGryaozkWVfiWs8NMk6HemE4ACppjPf922fwbN+LeCvgwhVn4QfX/RMgSzDHKvfXcpiJmqSS6qvo+gUut+Dg8iT63lWfFAMAFAUrtr0y9TYCDUGQEB8IEiJwODCb9It3X79yStrAjG6jxDQYo0UYAxlAkhBYkqipkjEO5pn7p9fyHOAISLrMxKfeY9h5E9BkyJU+Ivw1mZkyxh98lREQrScGmfODKO6cgDGUq6v/GL57K5yyBWOsiMwPr57RvQJmvlpl3iYVW3IejgNYqSKUZBBWqghJleGYdg2x4vUKFNmnD8AYycPgqlMCS5NwbAfZpwZc28ohFZKuILSyhdinVxDbsABmqoTCtjHMBsaBLCtLZa6q1FQMcIkwAdLPhTZwCyxNIvvMAWKeJktQ28NwyqSHkDFMdDOlsIOl1711qox+1LsYK4MNLA4EEZkTCBLiA0FCBOYSdtEkLdkrOFSnzdKeSRR3pNhrftUbO2chRr/HWat/dBXTNFDyUD6QZfnuep1qAcDOGghxERC+AsYuWoBDVu1eAsK3tNcXRGEXzGqkwLCRe24Id23+V3zz0bt8r3forhdcHWhnEwlZcMcvXa9nk/JyTJvZiwPcBA5ACqqIrO+qcdGsVwkEkBJl6gLrlG2WwlJbQjXlqHy3Ynb+gQycksUM4oCqmNYLWqkCeDrStoQA22FNBwF35Y+kyjAq6SQ7axAGRjWcSrWaROuKIrAwivJAFuZEEXJQhRRQmDBZSQZrxL9aRxjGcDVV9ePH/gcf/7tra8Z+tOLnS5Zise6OronUzKFDkBAfCBIiMFdwWa+/o8cV9p3pMbx6D+/r+Pk9mPjJTtZy3ludQgkI7REyFQFxyjaCx9eWJJb6UtDawyi8Pl63BLfUl4KVKiF0UjvKe6qpCaUpiMKLI+j5u3PqXuvgPz5ftR9HVWPy6vErprhDbngJSKNwHNK23ks+AkuTMEcLsNKVFveeig9auWEXTTaxUygtIVhjBTimDStTvS4lHkDHp08CQBrS5V8a9fXtoODLnr3QexNIXNwLOA7Sj5LomJUto/j6ONvHu78SD1S79uoySq+Ns+MZgzmSnmJW7xrsTIUU2gAUiZl/qU1B2HmzKvKUJaiebsJ+OqXia2OuhnMAIS4wSKWNY9iQNBlyRIedc5f9Hve1C5At1hKvIwE/fZIgIocGQUJ8IEiIwFzgUNIv3mNMR0AoSn0pqB0RNF92DAAyGWWfHkTmif2kW2hUR/T0LkR92pIzAmIDwWOScAyrxlLbzhsovDoGtSmI8Jp2RE/vqjE9U2I6SvszgF3tDeIYNozBbF0C0vf13yLcGodTsmAXSJ8ZtSnI7lvDJGSaELmZKiL37DBgOyhxBMkLtTXEyBw/gbd8eAWUqI6Jn+5kEQgrXXbpT8yxAiATPwonbxIxJEh5M2QJgd441NbGGuHZJRNyoLZUmBIWb58T2gclsDRJOud6IiqRUzqQfeoAyvvd3h5ApQcM3403pAAWiXYpUd3lAeIYhFQ5IMRNTQar6R0QwTE/LqdoQY7pUCrkReuKsvRP4bVxF/G0CyaJ3nmEom1XnwBJlQmh3pWCmSqydgKQJbKPQu5vifcYsRyMFiaw5pt/MN3tnhLfXtCNi2KxmvcFCTk0CBLiA0FCBA4F1CCM4lAJiN5Nwt788eoREL/IROaJ/eyBv+B6/w60fFddaljGtA6LYijvzcApmci/Mgq1KYj4Bb0wR/JsNcuX+hpDOWby1PTHx+LgvS8hl87i2I0X+p57YOMzkDSFTVC0mRlfRmxOFBtIy8hY8do230+yvxuElS77fga4vyPHcpB+dC/Th3ijCIGlSRR3TcBKlaoVNiWbuIhKYP1NYDvMqMsbPVESAeY0CwDhNW2sLHU6+DWwswsVsiKTahsoUrXkunI/HcdBefekO3IBQFJkQkQqpaqSJkNSZX8yIEnQuqMovEzSf3bBZMZwSlSHEtOhJHQUKpEVJaa7IkAASMl05fdI/WIA0jHaKVmMzMghFYFlSbT88XGV696DUt+kq8Sa9oeRFBl6T5Skezi9izdyRMuo4xcugtyA5wzFpfE4vt7ZBdWn3F2QkEODICE+ECREYLaYi+gHQFaSmd/ur3nfq82gRMEYzkPrCCO6vgtKnIhUqfhxJgSEgh43cVEvCq+Po7QrhfxLB6E2BZG8ZBkK28ZcXXXN0QLsvMH0Jryb5VTltwMbnwFA0i41OohKtMKcKEKJkQ6v9comvSmYep2AKep9N5Ss8JM8ncR5N1g5oMAcK7rKcwGQrrFcVERSZBYloeW65NpsYJpJkDYdpOB/W1QLoiSDUJIBlPdMsnQSUNGvlG1mr87bpmtdUUgSIVt2wWTVTWpr2BXRcRwHEkgFET/xU6gtIcgBhZzLcSCF1Gon2oCC0OqqnsixbKQf3Yf8SwfhGJarr4wcUlmjQgBMr0Sb2xVePkgIpCbX9M6JrOuEYzsovjoGK2+wSA69Rr03juS7SF+d8v4MAj0ze543Uh4uSMihQZAQHwgSIjAbzBUB8R6LPyYzwepPQ++t/W3SbaiVNRWOtnzgON/z8GW4LBKxOIHkOxcDIP4g6Uf3Ir91hIkP6QpbUmQyBkWCU7aQ3zrCdCJ0wq5HQL5xyV/iExd/GFpXBEo8wAgI/3+AiEMDixNkAuGIEQ/e08McL8LiOroCxHAMlg1jOO8SdfrBK/TkRZuOA5gH86RSRJKYx0RgcQJKIoD8iyNsv9hZ3QitakXmqQEUuKgYDy9BckqmK+IFwEUsyBsgDdW4fe2iidxzQ679ZF0hJamoeGYULTZea6IEh2uSEji2CdZIwZVO8SstBgjxMMcKcBzHJR5WEgFIsgQ7Z7DzUtKitYcRPJboi+j9Zb1cCiZJpQRUOLaD6Poudszs7w4Qrw8fd1M5qkGJaHBsxyWG1TpJKpL/+0levBgzwUx9aQQJOTTMOwm58847ccstt2BwcBCrVq3C7bffjrPPPtt326uuugrf//73a95fuXIltm2rhmFTqRT+5m/+Bj/+8Y8xMTGBJUuW4O///u/xB3/QWE5QkBCBmSC/dQTGQaIfkAMKYucsPKTj0QcobcClxHQElyeRe36E9ICpM5HyBMQpWZACSo15GA9KQPhUQfKy5dA7qmmB4bu2skmZri4BoO0TJ7Ay0pF7XmTHSP7hMqT+exeM8ULd5nADG59x9QrhJzlKQLTuGDmvVe3dElrVwlbJzAbesmt6jHgn96kEnwDQ8qEVLHpEET+vB8ZwHqmf7arpFusdK39OM1WCmqyaozViLuZ1YjVGcqQyBYBdtGCOFzw7UOvXyv/16m9BDqkI9CbQ8qHaiXT0X7ejPJCpdpqVK+Zd3G+JRrGiGxYg++SBmu9mOvDb17iW8pkMCdBaw5A0GeZEEZF1xBLdNi3knhlkaRa6r6QrpBlh0ayOtxJJ0RbGIMmSKxXprVqaDkN3vsDI9dhtjfcFEgTk0DGvJOShhx7ClVdeiTvvvBMbNmzAPffcg/vvvx/bt2/HokWLarafnJxEoVD9gzRNE2vWrMG1116Lm266CQBQLpexYcMGtLe346//+q+xcOFC7Nu3D7FYDGvW1FYD+EGQEIFGMZfRDwAo7U2j+No4szSPnt6F7DOkuRqfrkhc1AsrU2afBXrjyG8bQ/H1MSZWnI6AeLUOsbMWInh8M9IVJ9XizgkY+zOAKrPJyXs8ehwlGYQSIWH1W//jn3HLo/f5nndg4zNswgHcTqqBpUlGvMoHsnAq3hZenUtpz2R1Ikb9ybFeLx4vEbBLFvFUAWDnTUghtSaaondGoXVHfSuBANJfJLSyhZ2vkd+Fqxy4EgVxyjbr8msXTCjJAKxUCY4NODmDuH7SyIBU+S+sQueErt7oiTlRhBzWSB8d03aJTHmzOqdsw5wsMeM2ithZhFQHFscRXO6+n6W+FIq7Jn3JINkngdwLw9V+LTJY4zhJkRFYkoDWGUHx9XFSGmxw11YhG2pTEHbRZL8TO0dIm5UuweHEz//2/E/xl/d+1fde+2H47q01vx05pGL/J/y1SzUQPiFzgnklIevXr8fatWtx111Vv4AVK1bgsssuw8aNG6fd/yc/+Qne9773Yffu3ejtJX/od999N2655Ra89tpr0LTZtV4WJESgEcw1AQGA8f98A+ZogU28/KTrTUfw56e9NJQkETyqyWDdMR34f79j/1abgmxFzD+Qcy8Mw86UIYc0RE6tJTN20cTo97fBnChCUmRIqgQpqKLz0yfXvbbhu7ei5cqVbIVNyzABIHRCK+wcIR1Wpsysz9uuORGSLNVM+n6EaDaY3NSP4q4UzIkCsffmoLWHIakyomcuQPiENrY9j+j6LkAGsk9Xu/DW8wrhx5v93SDMyRLKu0mFDk0r2JlyzUqfF7fy2pjIKR3IPUe60nq7xQKo0XBo7WHYRQtKRAOkaiWNJEnke6w0bqP6D753Cg8q7qwHr6CXQkkESOqEj4rYDuycUfUikUDcW00uBVPp6yLpMsIntLvu5+joKNra2uqOxYu+259CJBiuansqIlla9UQxbTWWICBzhnkjIeVyGeFwGA8//DAuv/xy9v51112HrVu3YvPmzdMe45JLLkGpVMIjjzzC3vuDP/gDNDc3IxwO46c//Sna2trwJ3/yJ/jSl74ERVF8j1MqlVAqVfOb6XQaPT09goQI+IKfXILLkggsTczJcWl6RF+SQPLixTW24PX6xVACwqc4/CZoK13GyL0vwjHtmkmGb6M+/M8vwBwn5KLz8+tY9QJ/bqr5oCtpSZWx4Iun+V7X7q8/jsSaLshBtSY1QsWHAGr0IO2fXFNT/jvV9TUKx3Ew+cs9KO9Ns5QB36fFL7LiHTdvAkfhRzq8lSz89dGJkK9CqQ4SkDQZSkyHMV5gkQ0lGURwWe34KOIXLEL6N3vZmM2JIpS4DqdswZwoMX0INBkS18ZeDpAmf95eOwDR5WSfqfbR8XYXVpuCLtFtqS/FLO/NiRLUpgBL11FjMytbhlMwAcr7NOJJQt1o+d8m7evCn6/jUyfVvQdefP/Ld+JDn/kItM6IrwibnWei6KrSEr1jjgym7lV9GDE6OgrLstDR4e5g2dHRgaGhoTp7VTE4OIhf/OIXePDBB13v9/X14dFHH8WHP/xh/PznP8eOHTvwmc98BqZp4sYbb/Q91saNG/G1r31t9hcj8LbB4Yh+AO4KleTFizH2H6/DqkxS9QhI8fVx5vGgdUZZX5P4BbWpzNT/9iH3/DARVVbSKxTUtGxyUz+Gbt/CSiq7b6zVdExu6ocxnHM1WcuXC1h+w3m+1zWw8RkEj2mqMfHSe+Iu4zavMNXKlGsm9UMhIIVtY4xwUNEuAChRDUo8ADmio/VPa1e/dAxaZwTGUA764gQkWXI54AJwNZyjJGPknhQbN7U+N4ZyRNyrKSQtUXGdBYjmhqWgliRQqkRJZFWBY1Vt4kt9KehLEtC7ogif0OoaKyUg+ReGIUd1ls5Rm4LQQxqsTBlql4/hWeW65JCK2FndGP/xDlcjPvp7UZqDsMaLMMeLVSv4Qraq/6h0xTXHi4is7YDWbcEYyEJtCsIYyRMfmEnq7QES9VFIRMIpWZBUuVqqXInQRU4h6buZCEw74q144cs/R/ikdjiGhYmf7oSkK3WjiZTIO4YFOw9GqGjVldYeQnhNOwTmHvNGQii8AqIaNXgdfO9730MymcRll13met+2bbS3t+Pee++FoihYt24dDhw4gFtuuaUuCbnhhhvwhS98gb2mkRABAQrHdtgDHphbAsJPtu2fXFMlJJKEtmtOcP09TG7qh2PayP1uEFJQgaQraLpkGUp7SD4+fGIry/Hzq3BzlLh2yiEVoZUtkEMauw7+QUwnU285LzU9g+OgtDcNp2RBDqnTlt+qTUFXLxYqqrWLJiRNdkV6qEupN+IxW+LnjaJYOQPWZImF4LX2MNo+fsK0+wJA8pJlcIqmq7NuPcGrYzsk2lTxUDG3DBFzMtsmbqSWDUjuLrlaRxhyRIdjWCjvyzAC4iWg/O/QGMphcijHyCgzErMdllZRk0EEehNQW0O+/jLekm8AKGxzV/PEz1/Efl8AyDGXElGwpMgo7pqAMZgjaRaH5FrsnIHMb/dV0yw03q6AkQ9ZU4jGBYTEaW1hBI5JwilZKA9kIQEzingAbp1HeSDjKqsGQCJCqRIZJ/d3RfVTjuXg4P0vue6H1hlB6IRaYi8wN5g3EtLa2gpFUWqiHiMjIzXRES8cx8G//Mu/4Morr4Tu8fLv6uqCpmmu1MuKFSswNDSEcrlcsz0ABAIBBAKBmvcFBAD3hBRd3wklPne/FZ4oJN69pJqS6Ykh+QdLXdumf7OXPfDlkAolGUTHp9wpi/xLowBGUd6fYZ4K5liRWXR7Uw3elaAcUtH1pdN8twGAzJMDbLt6BOT/XfYlfPjES9wdabmKnlJfCtqCqItseFMWdEKg5/Z2sPWDlyj66STUZBCBJXE0Xbbc9xiTm/phTRTZPnR8/HH5ccbP62GNBI3BrKsixLEdOBkDcMC0HnJUY5VLvCCX9lWRtNrVOg9KMOn18dfmTtsEmACYpmi8ZC7/4kHXe+y3UZmg6f2jQmUAgCwjsDiOyMntyL1AqrUkSYK+IAq1PQxjKEcm+vEiqd7hk/3UyK1yDbZhAQb5LekLooBDGv7Va2pYD8N3b4XWHWXOsvR3pXcTd1NpIAMlqrt0KrnniZaGpt/K/WmM3PMiAkuTvlVP+RdGEFk39bwkMDvMGwnRdR3r1q3Dpk2bXJqQTZs24dJLL51y382bN2Pnzp24+ura7pobNmzAgw8+CNu2mSPeG2+8ga6uLl8CIiAwFQ5X+oUem58oJ3+xGwDQ+rHVkHW3fskxbWSfHWSRitDKVjT94TImZAUq3VkrrpjsNSfwC69pJ6LPsYLLrZP6LABA11+dVhN5ocg8QczT5GB9ArLvxiegJgMsnK33xl0dYen1GgeylWoYk5WjAtXUUPGNCWa9Hb9wUd3oaP6FERiV6+evXQ6rlfeIg6ikyS7/E++1eaMaXrJWT2ya/r99KB/Iwhgk5IOKbZ0iIRqOXhWZSpqbeFDBMfEgIRFgJawiuqGbHd8cKyD3/IjrnC7CtigOtT0EOBIKrxyEXbKqVSQVT47RfRnoPW67ce91xM9fBEmpCIAr95reA60zguCxTcw8r7hrgpFWO28AEknjMHFtpQRYimrkmmIB2CWTkWLmH1LpYRRYmsSXvv7XuOdxd2p9KlCTO3qt0fVdyDw+wFJIhOhGYKXKjIwoiQACqDR9PJjH+H+8DnOiCJNLz3mdbdkC4aLGKisFZo6jokT37rvvxhlnnIF7770X9913H7Zt24be3l7ccMMNGBgYwAMPPODa78orr8SOHTvwzDPP1Bxz3759WLlyJa666ipce+212LFjBz7+8Y/js5/9LP7mb/6moXGJ6hgBK2cg+1Q19H44CAgAlPrTMEfz7MHn11QOAAa+9hQcm+gH9EVxaG3hmugBDY9X4aDURyblpkuPQf6lg6z0FwAia9uRfW4Y+RfIqrDr/zuVRSusyRKyvycTTX7rCHHWtGzc+pv78O0na716AGD/3z4FrT0Mx7AROKYJkiIhtmEBMk8egOM4KLwwAoXz0OBJU2BJAolKzn8m5a18s7nA0gS7Xr0nhvK+DNteaQr6Nn/zkg/+/ue2DJMVfQVWtgxzhExyjuWwhnYMHrtwv4gG780ihzVSHVI0GVGayovD6yhLozDVVXsCgARJkeBYFXJTaZzn9Teh43IcB+lf10Z5gsc2IeAxwxt76HUYB7KEOBZMQpQr4lZKuuyKRolWtKgdYbfZGAjJzmzej10Du7HuY/5aIj/suelxaAEN4ZM7IMlVG3pvFQ5v1EahNgXR9gmSehv7wauuyiEv8ZB0BWpbGHKguhDQOsIIn9h4FY5A4zgqzMpuvvlmDA4OYvXq1bjttttwzjmkydVVV12FPXv24LHHHmPbT05OoqurC9/+9rdxzTXX+B7z6aefxuc//3ls3boV3d3duPrqq6esjvFCkJC3N7ymVVM5bM4UfMqg+MY4myC0zgiaLj2mZntzsoShf3iO9fWgng1T2ZJ7qzJaP7Yao999xbU9b2wGAJ1fOIVFX/jrL+5KwRovwC6Y6PmGv4kgAAz83TNQm4NwHAfBZU0146APesdyXF4TlDj5RRr8CEjhlVGUB3M111/alSIcoEIC7KLJqle898hLUACSZsv+jtwLK11i0SUegaUJFLaPuSYwV8qJi/pMRZ7sggljMEuiVBJxnuUnUuo+qsR0RDd0o/jGhOsY8fMXIf3o3rpGYvR9vj9NqS/FKlgc22HdjfkxR9a2uyJkAHHMHfqH58i/uX4talOQ2LZHNBRfG4dZ8VWRVFJ1I2lETMvuU1sYgUVxOI6Dpncu8b03fvjvP78fpx6zhni3cBE72IDaFkJgccJ1zTw5JPdRhjlRqClXptdA7135QIboWirCWh6RdZ3Qu6MIrWxpeNwCjWPGJMRxHGzevBmPP/449uzZg3w+j7a2Npx88sm48MIL3xKCTkFC3r44nOmX8kAWhe1jAKr5fElTED6xreZcueeGkXlqAOYwcSuV4gFE13ZAbQ5CbQ2h+MYE7ILBBKb8eL2lvX5lvi4C8tm1LH3CbOEHs3AKJsxMGfZEsW732/5vPIFAUwSBZUmU90zWJTm09JF+Hj2tk0VaXKkAz7XwmNzU7yJuVroMOaajno49vLYD0VM7a45BI0R8RYsXgcUJVp2Re2G4JoriOA7URJBpbQAgcnK767X3vPVKdSmaLjsG+ZdG6wpe9SUJlm7ij8OnoQC3/obeR7tosooenmTxJdJ0e69QmYLar4eOb0bhtXHX51Kl8Z33PiUu6oUxUkDMp2tzPVy47lz84Jpvs+tjsB1knyZRNQBVLxGu2ov6zXj1MgBgZw2o7WFIOiF9TpF0iZZU9w9IiQcAqZqmdMo2wmvb0fTeZQ1fg0DjaJiEFAoF3HbbbbjzzjsxNjaGNWvWoLu7G6FQCOPj43jllVdw4MABXHzxxbjxxhtx+un1VfNHOwQJefuhvC/DOn8ChzH90peC3ptAfuswZF1B6IQ23yhA9ukDcCqdToPHN6P1ylUASPqBhuDpAzq0ohn6whg7Bn0AR9Z2sCoLPs3Ak4PWj6yCviAKc7SA3AtEe0BdTM3xIibzaaz8xsW+1zSw8Rl0fm4dMo8P1FS0pB7Zg/zzw3BMB5IqMZEkHSsrfa2UPvqJJo2RaokoX44MeO3TE0hctLguiRn74WtEf8GB319tDTGxsZ+3B9uuPewytPI7F4WZKiL7zGBdS3m9K4LQalJe69VnuJrnLYwhuKIZpV0pFF4ZY91vJUmCYzuARCZNSSHaCiWqIVqZ8M1UCblna+0OvNE9r3cGTW/RlEpkXSdJrZ3Xg/SmfpR2T1b9VQIqlKaASzCrdUcRO30BtLbGugJTDN+91XWP6H01J4oY/4/X2b8BQnqcsk3SP9RdlbrocmORQypkXYEc0WqM3OSQyhoMBpYmSaqpaLrExZSkJt61BJGTRInu4UDDJKSnpwfr16/HVVddhXe+852+bqT9/f148MEHcffdd+PLX/5y3XTJ0Q5BQt5eOJzRD/74pCdKFIVXRkmb+/cfi7xHdGgM5lDcNUFC5LaD6IZuX02Bn95gclN/JV1gIHxSO8r9aVLBccEiV9kuJSCRUzuRuKC68qVpAvqwnqr8duiuF9DxqZPYhK13RyEFVCQu6sXQ7VtYIzOtI4Lg8qaGJl05pEHrcjtxWpkyim+MM1O00IoWFrWhglV6PGM4D2Mw6+oE610NU62Gn++KH/GInNblm5qZqieMXxO9elofCsd2cPC+l9hrbUGU+IlIEopvTEBSiaspHECOEFt+ivDaDibctdJlmKP5mhQUL+7Nv3SQtLznUNqdqmmeR636jeEcrMkSJFWumaC9WpOZNotLPbKHjO/8HqQf3VfzeakvxX5Ljmmzvwu7bDGC4BQt0j1XQuU/CVAkqC0h2HnDNUavG6zjkKoml0OrJJEGeXEdweXNiL+jx+VpIzC3aJiEvPLKK1i9enVDBy2Xy+jv78fy5f5lcEc7BAl5++BIEBBvUy85pCK0qtXluBla0YzCq+OMIABw9X5JP7YPxddJpMbPsnxy0x7kthCBaXh1K2yD9AiJnt7FHE95AhI6vhlNly1n11/YNsrMp9RkEB1/fpLv9dz+ka/hqg9/BImLFyP1yB6Ud09CUiRETumE2hbG6APb2HFiZy1kDf38JnqtK8qqSqg2QdZlxM4lKV1vfxtvqsfOGSi8NsaO551s6D2k+1BknzoAq+LhUVsVQ8Sdfoie0UVKPetEGBiZimjQOiI1562Heq6whVfHqh4rTmXSb67qGOixC6+NI7O5dgKnx3FMm/Rq8eSt7JyB0r408zOh6Pqr0yDJEib+excK20fhOA5xWTVtNsHTSVzrjODyr12FzS88Oe11UlDi4a0E4kWyxR3jhChxKRegGpmgWiJJkRFYmmBEkZIM8sJmhEIKqFDC7tRbmXqfUPLiAJAlVkkUWJJAdEM3sbkXOGyYd2Hq0QhBQt76yP5uEFaahPeVuO5qIT5X4FMjAFhjOb/V+OiDr7IwuBxQEVrdSqoXKkJWOsG1/MmKGht1frIOHtvMPucbjvEEJLi8CbGzuomniOMg+8wBSBVR6lSW2NQIKnFRL8Yefh1WpXKk7eoTkH50L/EQqUx4enesZjVOS0YBIlSk4/RO1MZYwRUViKzrRPikduS3jvh6f9BteMtyisRFvTWkwUwV2di1rgjT1URO7fQlFzNF+MRWRkKmQl3jMMdhfixUKKl1hJmAtP2Ta1xEynsMAEj9ag8Tn/KgpcBW1oBj2KBGHsHlzUi+dynkgILUz3aRZnqWDStdZqkLXpj63Oh2XPr3H2/4nlDi4a3wYeMybBT7JmAedEedqLle8JgmBI9tclUDAagaj3GQZAlWzoAcVBkhBoimxUqVmPCU17soESLYBQgJN1NVvRYAhE9onbJfjsDsMSsS8t3vfhfRaBR//Md/7Hr/4YcfRj6fx0c/+tE5G+B8QJCQtzYOd/TDGC1g9P6X4XBOTbRvhrezLSEHwwAcyGENweObIUkSYucsZL4M9KHLN1Kj+/Ikp+my5a6qDz8RamBJAmozEU8Wd04w8Z0S0fD1R+/EP//kO77XNHz3VrR94kRIioShf3yepQOodoQvzaQVPAAQO2chK3X0a2PvvRfFHROw0sRrQtIVRE/rct0DgBCQ0MpWyCG1Tpmpt288V8orS6yigp6fH5ddMmEMZOuWyvL23TVeG1zaayq49rMdl4aB+W8UTMhhDWqlpFkOayQlolU7yyqVyI+fEyoPb5WSU7bhWDZLp2jdUUgAS8fYZQt21oADt3u1uiyOjg+snPb6KH739Z9hcRv5LehLEq5j8d+nMZyHpLvTHV1fPI31tpnc1A/YNkp70nAch9nQMziEWNKqIl6Y6xg2ss8Nku68JtWMVP4X1aF1RUgqB1WxsF0wXeQFIMS9+Y+ObfjaBRrHrEjIcccdh7vvvhvnneeu8d68eTP+7M/+DK+//vqcDXA+IEjIWxeHi4D4NZSDJCG8uhWSrrAVYD19Bp9u8DqJ1ut3wZe+hla3ws5XH5z8tsXXxmCXLGhdEWjtZDWXeWI/C20r8QA6P3Ny3WvjrbDzzw+Df2RQYyo5piN8cofLDKze/fGOkUZyWKWFJCF65gJAkgipchzoi+KsZ4pUcfPkq0W86RcKv5W3n1U5QCJHkOWabae7lkZ/R36dgClyW4YgBxTYlQmRXodTtmCXrGoflwq/oqt8P7Lk1co4JRPlgWzFKl9hIlatO4rs4/vZvXPKNpySCSmswSlbzAdkKm2QF5/Z8Kf46/f+BQAw4TXV8/DgyTPt3hta3YrwmjZknx6sIZ1AVYBLwXvLeJH6xW7kXyR6K/obhQ1AlwkhcUC69UruhnyyrkBfnHD1zQGA5iuOg5qs9ZkROHTMioQEg0G89tprWLx4sev9PXv2YMWKFSgUaoVcbyYIEvLWAz9xhI5vrnGQPNRjAoA5mkepP01Wl13RakOzPZNs9Z24qBd2wcTE/+yq9qZoC0NfFGdmWPW8P4zhXMWWHRWXTZKin8rds7hrAk7JhhSQEVzW5OoPQysD6qVf9n7zSQRaIuz4xTfGmThRXxB1ifz8dCre+2SXLdg5A9ZEEWprGOZonplp0TGpTUG0f3INjJE88i8eZMewSybkgMo6tOa3ugW9fkZkPAKLEzAmir4pCip2VVuCiKz1t+amVUk8ZkI+6nl6wHFQ4gy3Ius6fYmTU7ZQ3l+NcvEGW8GVLYifvZCdi4LXqFDdR2BpEnpPDPkXhlk60hwvwjFtaO1hGGMFOHkTPd+s7wnjh6G7trLuvvVKjLlLhmPYsHNlSKqM0OpWSEq1j5BTtliqiaQmW0AjW1Pd84mf7kTh1apGyOvM6hg2rGzZlVayC2ZNNEqSJChxHXJEQ2h1K2KcbkVg7jEr2/b29na89NJLNSTkxRdfREuLMHQROLowV9GPwmvjNSZXAGm5bqWKsNLEv6L5T45H7hkS4eC1Jt6wuJIIIHhME8IntGLipzsBkEkivKbNNQF7w+00hTIdASn1pQCLOHKqwQAyj++vZiksBxOFFFb9lX/57ehDr0FrCbGOvJOb+mGmS3CKFiMgalMQaPIXygKkI+nBfyEmaXwrd7UpCHM0zxqsqU1BqMdHoEQ0xM/vcV2rMZwj+grTRnHvOCRFRn7riMtoKnbuQmQ27685v50rwxgpwBwv1K2S4WGOFWuIpZ9xGRN8TtFss/jGBNL/59aneIW1ftEAfjuejPAdYEt9KRYpKe/LoLh9DMXtYzV9eKgpGxFvJiEFFRS3j1VTPrSfTUiFpMkzbhY3sPEZNmZKQPjxA0DuuSH2m/OavEXWdZJy3/60i1RJuoLI8WQe8XNu9RKtGj+Qggk1GSCLgYUxZsJX6kuR731d9T7ZQRNWwYBkg1XcOEWLEOayhdzzw7DzJrT2MMJrhGPq4cCsIiF/9Vd/hf/4j//Ad7/7XeZuunnzZnz84x/H+9//ftx6661zPtAjCREJeWvAsRxX863ZEJB6uXZqsGWOFzH+cDX9yD+AefJA/813PPWaU9HJPPfcEMwJjyV4BZIqo/hGtUqGR+KiXljZMsZ+8Cor57SzZRJ2NuxqhUFQRfdf1w+xpx7Zw9JGjmnj4HdeRvlAFpImQw6orBpB7SDEoV5flVJfCo7tEJGfJCG4vAlKPECiGT1xlPdRu/UkYmd3MzMtL4qvjxMthEO+U0mVakWvJQvGQAaSrkBfGKtZjcshFS1/urIhzQa9h15MZalOrxeoFc2GT2pnolIrU4YxlGO6FzlIKl78mqbxqDWzG2LVUOZEEUoyCCtVhNocghxUUD6QhZIMVESo5YoIFew3IUd1QAJW/e3FSBXS3tPVxYFbfg8rUxF0RzRGQqxMGY5pQ0kEoC+IMgEyjXQBpKmelSoheGwz+w1TeKufijsmXJ17eZT6Uux8bP9kEPCQ8qn6AcXOXUgI0N4M0wtRImRNlphIlSK0qhVNlwizssOBWZGQcrmMK6+8Eg8//DBUlQRTbNvGRz7yEdx9991v+kZxgoS8+eHqfFsprWwEjmX7+hUA/t4QbNXZm3Dlq3kCYo4VCHnYSey3vfoPoOojYWXKyD4zWBOST1zUi+zvBlkaQkkEiHiwYo3NO2eaE0WiLShbgCIzDYHSFIQk1W+Pfs8nvoUrPnAFu87RB7bDHMvDTJXIZNkURGBZsn5qgYOVKqLUn4Zj2ux6eSv1elUSQFXvUHh1jFUT0QlCUmVo3VFfEzBzrMCiRPTYanNwRt1PvUQqeFwTAov8nwF23kDmyWp/ofzWEfZ9eCMtZqqE8t40rPFKVEWRIckSpGC1Ksl7PTziFyyCNVFE7vkR5ucCkFSKN9JA01q0HJz/TF8QxcPP/Ax/8b0vN3I7ABBNECVWfNqMjpM24LNSVeLMbxdYmoRt2jD2ur8zpvVIuM3OvCJWoNp52Tjg8TKpOL56XWN5BJYmXT4pfnogvTdOIjLjRaKdCRKPFiUZgNYSQvLSY2qaSgrMDQ6pRPeNN97Aiy++iFAohBNOOAG9vXNfaTAfECTkzY2Zpl/qRTsCvXEEj22qed8xLKQf21935epnn04nUX1xgj1wqbgyekon83/wmpFRGMM5pgmgfTuohwTtliupJK9ePpAlwjvLhhQkoXZqm16PgEz8bBckXalJFdgFE2oiAEcClLDmCpt7SRJF6pe7GVlSm4KIbehGeTDHPreyZShR3ZdoTW7qhzlWQGnPJDsPvTaAWJJXG9aRfY0DWWgV3wq/8TSCmkqXOj2D/H4rpb5UjesqhV0wMfTtLYQEOAAch0RrFkShL4qzVbi2IFr1janoRMg/3ZM7hSTLcOxqJMDOkOiGXTRJwzhdZlbqkiwjr5dxzOfPavh+bLvxESRDcRexUWI6gsc211y7N/qgLYzB2J8hlTiGDViOS8ysNgURWtXqOo4xmGXEReuKsmPxehaKwNIkAovjriinF34pQq8zrGM5kBQJVqZcU/YOkMgNrSSLn9/jaQ4pMFc4JBJSLpexe/duLFu2jEVE3goQJOTNCRpFoJhqIqpHPKabvFzup5z41Lu/HwEBqhNnuT8NvZLrTlzUy4yhAPKQ5leDdFKmn7V+dBVLXSQu6mXt3lkvj0olgJzQWZj6r392K77zs3/zvabUI3ugxHQiEC1byP2+eg9phYTaFISVKkFJBhBc3oT4+YtcxyhsG0X5ACEazJG1TqUKuXdVfw5i0z6C/EujKA8QoqUkAoDp1JRu0vtnTZZYKsB772eCRipdpip/rbcvNY+zM1WreSUZRLhi/c1//37wE3c2f+h45CpN9oyRHOysAStdhhIn5IN1/KWVIJqEnq83LjC95ZLr8cGT38siUVpbmJUEh09sY3bwfvfDKhgo70nDzhsszcRXSddUtkxB3B3HQf75YdfncliDpMuQgyorqeXhR4gnN/W7uizzxnd++08VnRNddA8fZkVC8vk8rr32Wnz/+98HQCIiS5cuxWc/+1ksWLAA119//ZwP9EhCkJA3H1ydb338GrwEhcdsSiynytuP3PMi7BKxkpY0mQhDm4IILE7U9DChDz/6gNR749BawwguS5LW9P1pTP5yN9s2fuEi5omRuKgXxV0ppH/dD2OEVJqgRMzC5FjFgGtd55RW2rRfBwUN4dNVKRXPUigRjZTPeu4JBe07Q23ceXgjR+x+3fcyrIkCy8PLQdVF7mj31/JABk7Jct173pCtUfCdjCn430Du2SFiguUDP08O3quERaIsh/wnAVJMg9YcmlZTYo7moba6+61Ez1wAJaLVnJM6hvIl3o3Y7XshQcLeGx9njdwcg1TJUHjThrzeRQ4o1ftUMVWj35sc1hBZ2+7yjOFR2ptG8fWJuseGJBFxaSXi59XZBHrjUJpD7O/cKxL2ClaVZJA1OvRuW+974VM4AocPswpf3HDDDXjxxRfx2GOP4V3vehd7/8ILL8RXv/rVNz0JEXhzoV76pd4K1q9leaPHN8cKJMdNfRQARE7tYB4Ck7/aA3OUtA6XggokS4ZC/QVkySXIBEhqByCTSPK9y6B3V9MK5QNZFwHxCl0PfvcVUrp5IEtC8AAQkKG1hxFYloSkyHUJyL5vPAWZCy+bE0XIQRX6giisiRKz5eYf0FRfYRdMZJ5wi0jj5/Xg4HdehtoUhF2yGAEJrW5F+jf9rhJRGtoee+h1WKki60eitoQQPL4Z5d2T1RbzXGqiXvqnUXjLfvnj1BUge3xdWLlx3oAUVJF/YdhdbQIwLw99cRxyWHM5bU7Vc4YSkMCSBILHJGuE1Ty8JcozrWwZ+883XCkIvSvCUmaEgCoo9U2SCpK8yRrn2QUTsq6Q6pGMQS5WlSFHtZpon12w6t5XFumh0b5K6o+SGGrSVtw5AUmWmLZEbQkSkjhZQqmiC1KbgpAUGWpbiJXoqk1BohUxbVITbFWF2WoyWPP3fzhMCwUaw6wiIb29vXjooYdw+umnIxaL4cUXX8TSpUuxc+dOrF27Ful042rroxEiEvLmQGnPJIo7Uuz1VM6Rs33IVI9XdeG0CwbkEFmZ693Eb8SxHJT7K91FTZuVPlLPkKY/XMaON50ZGUBcVyf+8w0AtQREXxRD5jEini3vTRMbasMBdBmh41ugtoYwuL0fKz53ru817bvxCchBFZFTOomAVQKMit4ksr6Thfz5SZ+fpHjQKMDBe18iRKZiOQ8QHUFhG0kxKckA4uctgtYeZiZtVG+gtoYg6wqS712GwnYyidCICsVUPiTTIf3rfq+zNyJr25HzNA90XRMnUOZTI3bJcjWPYxVICmlAIodV3341PKb7jRZeHUN5f7bm8/JIDsa+DDln0UTP3zau8QDI967EA1CiGtERVWzb+bJzOapX3W9BokbWZAnh1W0oD2Rc168kAwgua/K9Vr9oE/MBMWwYnBkYIx6V71tpDsIaL8JKlZiWRI7rMCtN9yRZghRQEF7b4UrbsFQkADkRgMql62hPoODypMsxV2D+MatIyMGDB9HeXtvWOJfLifCVwBEBfZDz2oDZOllOdXyAKxH1gCcS7MHqOJDCGrTWUM3E6Sc69SMg1mTJl4A4NlnRZR7bB2M4D6dokpWk4UAKqZB0GVa6hNY/WVH3uga++QzkYMXJ0rJhVDQYWlcUclBhBITXnZjjbp8M3uytfCCLif/aQcR9ySCCy0jK6OC91d4voVWtiJ3VzdJUdkV7IgUUaG1htF9zIgqvjiH1s11wyhYcw2YTUtOlx8y6Z0eNmdxYga2Ac89X+9B4tT3e6glzrAC7RDwklDjxn7ALJuyyRUS7yQCsydKU5MOvc613W7+US7k/DWM4B8dyANPGPzzxXdz22+82fA8Gb38OdsGEkiBjtNIlEn3jiJVjO7DTZVIJ0h5GqUJCmEndrhTyrxysVot0hKE2h6b8+5JkyUWci7smXAJbPtLGN1kc/883YI6S1JzjOCzNZKfLRKuSLcNRZTgFE9nH9xOjMa4BLioaIjtnwIkHIElEzAxILLUlcHRhViTk1FNPxf/+7//i2muvBQBGPO677z6cccYZczc6AQEf8Cp3b+3/bMvo+P4jXlGgl4BIuoK2j5GO0jwZAkgunLp+UliZMsYeJL4TSlMQ8fN6XO6bLgKSMzD2w9fYtfHVKmpTEMVdKbJSpQ9eySGag8rkWi8sf+/7vo4/OOkCqC2kzBYOWJmrX7nwwe+8TMprW0KsQsAvlUC776pNQSQvWYbCtjEXAQmf3I78CyMobBtlIXcpqCB6Zjeip3ZCjmrs+2RluLqClg+tgBKfXak/IxH70jBH8q4SUL6E108LQKsu+BU/H7qnVvFyiOhWaD8ggEysoVVVs0YzVUTuWbfAEqi9j6mf9TFBLgBo3TGU96dhVCJP+w8ewBl3faDh69/z9SegqdXSXG9JuDlRcqU/gsuSMDkNFd2WRqMkCUzTlKhjy8/DK8qmoMSy9eMnQPb8TU38bx+LxgFA8JgmMtbRAjMRU5uDQHOQEHDLJpUzXPWOrCuQKyTDLlvEN6UpyISpU/mw8KjnLyJSNocHs0rHPPXUU3jXu96FD3/4w/je976HT37yk9i2bRuefvppbN68GevWrTscYz1iEOmYows0tFvem2YGRXJIg9YVmfGDwevtwMP78FHbI1CitSunxEW9KA9kUdg+RprATZSIrXhIRfMVxyG4JMm25R/IckhD60dW1tWw2CUT4w+9DrtgMgJy4P/9jnzGtye3AFS4lhTWED21E5Ck+vqPrz4BOKTCgZaR+pVWAiRsXeqrVOJUOt363eORe150NRMLLE0yd1GnTCYIqndxTBvGSB5aVwSSJNWc19v3pdHvlLex9x4LcFdB8KWf9XQZ+ZcPwilbrv15Isj//uyyheBxzWwBRo/pl4agn/Pj9fO1CCxNIvPEfpZS6Pm7cxq6DwDw71f/I8475RxYqYoDqyKj8/PrXGXG/G+xzPltSEEF0VM6AUiw82UYQ+6ITeuVKyGH60cQHMPGwX95mb32fgfUBZgXvFKC5u0RI+sKzMmSKzLFRLdORbQcJp9pnREk/3CZK/pujheZiRsPFvWqiJwBQkhpmftU0Hvi0HuiruaRAnOHWZfovvzyy7j11luxZcsW2LaNtWvX4ktf+hJOOOGEuR7jEYcgIfOP7O8GWW8LgOuDEdbQeuX0nTxLfSkUd/mbF3nhF5mYKm8/uamfmGlV9A52wYQS1dH5hXXMS4DuX96XgWNYbDKj5IUei8IxbAzf+QJbuQJVsR5AwttOmeTwpQBJvSixALTOMD53/434118+5Dvefd98CpJJSgy9OhSanii+Pg7HsBFYlmQmWMnLj4HeXpsG4aM6NHIRWJpEaVcKZqpYW/7ogHVjdWyHVdrYBYNVkUiq7Kv5cAwb6cf8jePYNj7lnNORGZ4MlPdlYIxUtS5KnJQg84JV2tMHALSeGCl/rnQG9hO2muNFWKmir+mWlS7DHM1Xxl613s8+OwinZM1I53HK4hPxv9c/4HJbpV2CvWlALzFQW0JQEoEq8bIcODKgVaJeSjKIliuO8z0vLQn3azIHuEuz6Ti8hJE1eazoW2grAAYHCByThBIP1PT74aOMjWByUz/K+zOMYPpZ+FtZA3JQYaTtUEXQAo3jkHxC3qoQJGR+UN+PoSoKnaq6YDr4PUwK28dYC3O6Des+atgsFRNZ1wG1OejqfAuANYHzikfJARym/veKHUMrmlF4lVhXO7aD0o4JWNky6yFCS2XVpiCMg3lIqkwMqWI6axoHTF0VMfD/fkfISlirCUGTaIfj8jAByMM3ckqHr5cCv5I2DhagtYVI4UHK3RcmsDQBx7AJAbMcWOkStI4I9IWxyrlTruNKmjKjhoKR0zqR+e3+GvfMuj1suFQbf35zoghJlZkegZ/cJjf1M00GPbY5WoDaSibpwOI4sk8dqGn5rnXHGEHxghpy0XMrUR3GYHZGEQ+gWlY9lbiZ7yJLQQlj/IJFLFpT6kvBzhkwaToxpKLri6e6jLn4nkl+Il21JeQSeyYu6mUluHbRrH5PDomAuKpguN+NnTcgV36r5YEsnEpFjhzRoHU0HvWc7plgDBOPFTNVBGyH6X0oaENDQT6ODGZFQp5//nlomsaiHj/96U/x3e9+FytXrsRNN90kbNsFGoJdNOv2C6lp2lZx2WwEs3lYeVe05b3piqCNc/KcKKLUlyKlf4bl6nhKDZ78xk8jLX45acdxUNpJbK/lyirMnCgycyfqOukUTeIWWulgC9QnIHu/8jgC3bGqS2svKRV1ShY7Hz22t+MvLxL03qeqi6oFOaQAsgQ1EWDjpX4dxmC2Gu53wNxgA0uTKLx8EHa5Wpbsl58PHpNEYEltBYN3RQuQUHnyD5b4bsujXmdXnrjwnXL574qv1PGSNoAYq1HdiMs59me7kH9l1L1tRIOVM2bk5QG4/Vz8GuipTUEUd0yQnjSVbsUUsbMXEtfa/RlGfL3W+8HlSeSeG3Z5ctCIBr8tPaekyC6ztakcTM2xIlDhNFS3QbU1PFz9c5YkAEmCpMmIv6PH97h22fJtXFgP/HXw3xl/H+v9TmYafRFoHLMiIaeeeiquv/56/NEf/RH6+vqwcuVKvO9978Ozzz6L97znPbj99tsPw1CPHAQJOXyot0oJrWqB1hlxrdAo/CYqvSeG0PHNNe83AnO0gNwL1VWil4B4V5aTm/pRfGMCVoboHxzTRvDYZmK7vijuyrvHzulG5rcDNQ9TflKLnNZJqiocB+lH+pF7gaQT1KYgc8CELJGqjEqrcSWiwwGpFjiYHsfqvzrf99oGNj4DOayxniuAVNF5kGZyVKDJCyrZ2DcscOX+qcGbY1jIbRkmUSEbgEwe3EpIA2QJkq5AkkhEhzYuAwCtK4LA4gRZVdu26553/X+n+tqie+Hb52NRHPqCqKuraT07dXrP/V7T752myHhNidoUZLbefk6bPHmhBNXiwvzekH9oVSuu+tqn8d9bHpn2milGH3wVVrpaURJYmoTWHkJoVSvS/7cP5mgB5kShGrWoRBoAQiACSxMILIq7UlreexA/f1ENeeDLp7WOMILLyW+dNgcESLWPHFF9qyGps67SFHTdEwBo/cQJGL3/Zdd7fm6l8XcshKRVI0r5l0ddvy0/SDIhLXbFUbW8L11t3IfGUyxjD77Kmu5RaJ0RNF16zJTnF5gdZkVCEokEnn/+eSxbtgzf+ta38Oijj+JXv/oVnnzySXzwgx/Evn1T53GPdggSMreYScrEsR1XDrjlT1b49nWYi7HQ/iB8uN7OlSFHyPniFyzCwfteYhOKrCvEA0OSajpvSqrMIif0QS/pCsIntLKOuN4ow8g9L7rSLkB15e04DpyiBTmgAjIgqQqUWP3eLwBw4NZnXeZnfJ8VNk5NQXBFE+ysO40QO2ehK41AUy/GeBFO3mQrWUmT4Rg2i5woUR2SJruFjrqC7r+prvRd1UwNVFh4W7UDVSEybUbIr+p5lPpSVaMz7j0/IuunaaDfg50z4FgOlLhOIjmyBHO0UENoeDiGDatS3koJ3sujb+DsP7l4yuvlYZomxu5/xfUeT3h4QbAc0iBXGuBRYuwPB6W+Sd/0DY9SXwpaRwRyRIOVKiL/yijR8jgOlKgOx7KhxPRa8uiAVFxVwEer9J4YrDTpGu11Cw6vboWVd/8Op9Jj8WBEnhMC8+kzAK4FQr3y3MlN/TCG87Bz5ZrPAJIqbPv46mnHIzB7zIqExONxbNmyBcuXL8dFF12E9773vbjuuuuwd+9eHHfccSgUplccH80QJOTQ4OdMOR14O3IAiJ3dXW3oNQfwhm7pQ92lpuc0HLxugD54lXiArUz5SateyR//QOW7ufJmXXKImFsFlydR3JFyrUKp+FRSZUiKVJeAPPCpb+OCntNIeWIlUsHfOz7qET2jC9mn3fb1dMUPkBUuJTJ2psxcJrW2MOktU6zk8x0gckonrKKB4raqSyUftrbLFka/W51Qpwppe0lFzYqd0zF4YY7kobaHa96vV2rpJR9qaxiB3rhLbExB01VUsMuDkh1vAzTbttH8rqX1LrUGT93zK6xcciyrSqJo/+SaqkNr2ULh5erfFP3d8dEtL7mwssRbo8x1r/X+Vqn9O0BSkFR/5JgOAIf8BiSJWLIHFOjdMYRPaocxUut5QhvOaR0RlPpSUBIBKMmAmxhwYl1+wTFV2exUOrB63/FU+xnDuZqmeBThk9oRXd9VdywCc49ZkZDzzz8fPT09uPDCC3H11Vdj+/btOOaYY7B582Z89KMfxZ49ew7DUI8cBAmZHRpZwTTiIjnXgjD+2JFTO5kldGbzPthl27UtjXBQ8zGq2ucFdJSALLh+vWvf4q4Um0i8Kzq/7rRaVwQdnzoJdt7A0D++AMAhxKSSTqHaD31JAk3vrNU9AEQrYOcMyBEN5niR6S/84KqiqEBfnCDW7/vSrBrJLpiQNAVaW4jtx5Om8EntrG8JbZAXPXOBq4SRF7EqTUG0fKC20qKeq+Z0K3YvvKm7ehMTJQvGUA7lgQwxuZMq6QOOYPLCXz7CRVHP6n2qHj1efOw9f4Jv/dEN0BdEXRECOaZDa6sSKm+KSO+OIrK+C/mtB13Xzu6T46CwfaymsSIjcxWy7xKYFkxY6XJNs8DwmnZy/QsimPifXez9esSbN3+TVImJWQNLk6xiiIfaHKy2NKjA72+fr6xplHTw340xmINdqCUdgaVJqE1BRE7pqPlM4MhhViTkpZdewoc//GHs3bsXX/jCF/DVr34VAHDttddibGwMDz74YMPHuvPOO3HLLbdgcHAQq1atwu23346zz/bv/HjVVVexpnk8Vq5ciW3bttW8/8Mf/hAf+tCHcOmll+InP/lJw2MSJGR2oH/4si4jdq6/mMwLr6HTXBIQb1WE30OKtokv9aWIC2bRJJOwIkPrCANOZUUZ0ZiBEhWixs7udp2P7+vCPwRDK1uQ+hl5iFO/g/C6DiQu7AUkYPBbvwcsB3bZgtYVgTlSIOcG8OffuQE/fvYXvtc3sPEZyHEd1jhxwaQRCiUZIJOKKkOJakx4WkNAKqtSPuoTXN4Ec7QayVSbg0xcqS+Ikkl+7yRgVh8bfIQj/et+FHdVz9P8x8fVEKMaZ9CyBUlXptQBuaqWyhbKFWMrvzSY1h0lpnU+YkMvkVTiARjDOeKGmgxAawszLxV6zbwBmXf8MyEeADDxq92kN05PjE3SfKmza7ySBOo3Tw3yeHIHwHUcL9SWEJLvWYrMEwM1370xXiBOuxXiwacDQ8c3o/BabaqLup6qTUGobWEigJ3kXFB744BFSBA1muOCiwyBpUmET26H1lq/f5Pfdw0ASnOILSLi7+iBpMnIPnMAVqZKMsoHssRN2HNOANDaQqyTscDRgTkt0S0Wi1AUBZrWmDXuQw89hCuvvBJ33nknNmzYgHvuuQf3338/tm/fjkWLFtVsPzk56Ur1mKaJNWvW4Nprr8VNN93k2ra/vx8bNmzA0qVL0dzcLEjIUYjpOt/O1bFpQzAKqlGwJstQErpLRGgXTASPayYPZUlCuX8SSkyH2hZ29VWpF+p1ExDHFWK3i6TFub44gfh5Pchs3u9Kv1AXTjmowjFsdF67tu717fvr37JUCetcGlQhBRRiZV/p6+FdtdOGYNNVJ5gTRSjJIIxBollRYjraP32Syw01ft4iBI9tct0DfmU+XTNBO2fAGHaLDdmKvTLB+FW50MgP1bz4+T7Q0mEKp2QTQS01u6tUM8kBUuUjh1SEVrbWJcF8076ZEo/UI3uqBKkjjOKuSTiG5Zr4aUmqn4g2/o4eZH67D8WdqWpZLLcv3ZaKmr1iaKCaPnRMh0W4KJouXw5jIAtj1D+Nzv9tpn61B7lnDrCOxwAhalpnxCUctfMmMxVrxHG0kRSLktCJb4iHdHkrpngCq7WHXQJmgaMPh80nxNsu2Q/r16/H2rVrcdddd7H3VqxYgcsuuwwbN26c9hw/+clP8L73vQ+7d+9Gby9nfW1ZOPfcc/Gxj30Mjz/+OFKplCAhRxmOVPpFTQZcbdn5SZZ2A1Wbgiy37g3ne6tk/MZL34+d1Y3izgkYQ3nfBmxENJlA7IwujP3wNZaWoVUEckBhngX1Sjj3fmkzJEWCFNaghDWoHWFoLUGU9tTm/b1iRidvkpz9whgkgK0wA0uTgOMgVzH9oukgoJoCkAJcJEWW0H7NiTXX7yUgmd/uZ5UKAADbqREnAmSVHzurG8HlTTXRK4Cshu2iSapBxorMnZa5yFYgh1TWUp7sWNG18I8hhehrHJss0eWg4uuJQmGmSoDj4Jx/uAK7DjYusB7Y+Ix7fLZD/lNkNh5JV4jPTDLAogV20YLeE4MS0wDbQXl/1tXsTYnppDLLxxyuhkRWyrx5QgAA2oIooqdXUzpehE9odfXrmdzUDytdRnFHNTrCvD4sh/ztaHJNF10KX++WOg0CAUDvTUBSpBqtDQXvXEsb07F9F0QQWtXqe10CRycaJiErVqzAV77yFbz//e+f0gdkx44d+Id/+Af09vbi+uuvr7tduVxGOBzGww8/jMsvv5y9f91112Hr1q3YvHnztGO65JJLUCqV8Mgj7rK3r371q3jppZfwX//1X7jqqqsECTmKUNwx4Zow55KATPzPLmaMJCkS9F631wRNpXhXjo7lENHdojhKu1LsmeYtwwSA8Imt0DrcD2iK2IYFGPrH5wFUw9tUXJjbMgQlEYCsKzAO5qtt31UZkiITgaAsYbg0jnUbL/G9Phr9oGkRgHRwNUbyLKURWJqEEtNZiWGpL8WqKQKLE1BbQuT+26QvjFUwYI4WmTGUkgxCjVf3548FEE1NZC3JoVPnTGMkDztbJiWkrUEYo9UIBE9MvJNN8xXHQ00GmD+H93PevyT71IBr9a21hRE8jlSDJC7qRfqxfSi+TiZJmvKCBDJJWmS/6OldKHHRH609DLmO90ypL4VfbP0/XHX3530/98PQP71AfDqK1W6uZBAOi1pBgq/gmjVqo51gVbl6DBuAIpFKD1VmwuEpYTtAJXpBK6ycsu3SffCVLjxxKGwfdREoJpSWJEgV0iaHVFh5E1aqOmY5pkMOa+RvaWEMkqePE99F18q6q1Ho74xqjCBJUOI6Me7bnwFshxiieaKlh1KqL3B0oOHyg3/+53/Gl770JXzmM5/BxRdfjFNOOQULFixAMBjExMQEtm/fjieeeALbt2/HX/zFX+DTn/70lMcbHR2FZVno6HCLgjo6OjA0NFRnryoGBwfxi1/8okZ/8uSTT+I73/kOtm7d2uiloVQqoVSqrpbT6fQUWwvMFnMZ/ajngglwIf1KCS49N288xZtOBZcTrUepL8UICK9zMMerk2o9AlLYPkr6foCsyOkYqGW2EtfhFE0Yk6Vq1YkDpuPQOsJTlt/u+/ITgAx033gGW0HaeQPGSL7GQMtLQCRJIuW5garuwnEcGCN5lw/FguvXM0Mw77G8pbV89ENbEGXt37O/r/7t0iZx9N4GliZhZcqQoxpgORh/6LWa69R74q6GgXbJQuGVg5ACCpyCiUBvwuWuWupLYeSeFOy8QaJIgcojTart/ULHBNT//Q3+z2tY8If1uxB7seOh57DojGMx8d87YWVKhGR4WtMHliZd3Z4peJGoOVGs2PKDERalJQQlQhxEizsnYKfLcByia6Cl3X6gDftcnie2Q8zqKoZ1vPkaAJSf8DH9qpAhOaiy+2kXTLLPBIglP410KcTR1ylZsCul3nwTQJ7USKrMvmM5oDBvmuqYSlDiOun6y2lOSnsmoSQDrKEiQGz362li5hJ6dxShlS3TbygwYzRMQs4//3w8++yzeOqpp/DQQw/hwQcfxJ49e1AoFNDa2oqTTz4ZH/nIR/Cnf/qnSCaTDQ/Am7JpJI0DAN/73veQTCZx2WWXsfcymQz+9E//FPfddx9aWxsPyW3cuBFf+9rXGt5eYOY4VAJSr/KGTqpqawhKPOB7bKpVsEsWlCRx+Ayf1I5yfxpKTK8hMN5j5LYMMwErK5ksGDAGczCG85B0mT1kY2ctrBlb8NhmlHZOQI5qsFMlYr2eMSDHKg/f5mBdAvKvH7wV5594FiBVSQKFMZSDMZJnD3RvGFxfnEBp1wQcmfydFV8fh5IIkBRQRIOZrgoilYjGrMqtdBl2oao7CB7XzFwr+fPntgxBDqgobBslPhB9KeiLE5Bkokfgo0rknpkwD+YBTxag5coVUMK1Lq10RW4XTGgdETKZVqIApb4UGysAhFa3wqjY74dWk7/9xEW9MMeL0/72HNOGrPlbrfvhm5/8Mj7zR59A/sUROH0mRvu2s8+UuA41SYSblKABYASEECVCBge/NeSanOWAAiUeZOSi5YPHM1InycSvg07YOndctYn4mHh/xzzlCZ/UVpN+KfWlquS1Iu2h3x+PQG8cuWeHiEA7RLQ0kqa4mjtSslk+kIVTMFEukO+Cam8kTYGkVt1defDtEcjn1ZErTcEp02UzgRJWEVnfBStTRmn3JHFybRA06iYw95i33jGHko5xHAfHHnss3vve9+K2225j72/duhUnn3wyFKX6QLHtihBNlvH6669j2bJlNcfzi4T09PSIdMwcIP2bvSyMrndF2ATR6D714FcC64U1WULmyQGU+tOQJAlmqojQcc0wRvJQ28IwD+ZJJUmqRCYLCdWVdAX0we59OOeeGyKNt7oiMFMlhFa1IvnuJa7IS6kvBcewYGUryn2nsiKsrJbVpiACSxJI1im/3XfjE5BDKuLn9CB65gJ2vVbBRHHbKOyiCbU5CDmoushTeX8G+VfGkN86DKdoQQoqkHQFTkX/oraEYI4VakiLY1go78u4qjWYpXkl8lTaNUEe3gppqOdYNgvPq81ByFHd5UtBJ13aWI0ifuEi38XG5KZ+lPZMkmhMZSVOJ9zA0qSrQoO+5y3l9SuhDZ/U5ip9BWoXQNNh5LuvwM6Va9w05YCC0GoifmS/l4qHSHFXCk7eYC3maeTBLpgswmAXTBd5TVzUy8TTfm6tiXctIQ6+la7FFLyo1evkC8C1vZIMsqolOaAgfHI7ss+4/WMSF/Uit2WYRQJLfSkm0gYAtSXIJnJ6bGZaR6Mo9HdeGRv1w6mH4PIk+53QdN/hQD17dgqv4Z2IhBw+zGsDu/Xr12PdunW488472XsrV67EpZdeOqUw9bHHHsN5552Hl19+GatXV93sisUidu7c6dr2y1/+MjKZDL797W/j2GOPbaivjdCEzA0aiX40Ymzm3Tf/8kFXu3G/Y2efPoD8SweZ7oOK87yVFEB93wNjMAslpkOO6q6JjTaw4yfC4HFNCFRKRVnkpVLuC5BqATgOq8SIntqJj3zt0/jp4z/3vWZKQDo/fwrkgILUI3tQ3j0JK1OdBNWOMNo/cSIpR63AsR2M3P0ijIEM0ZvoCiRFmtJUDXD7UQSOSUJNBEnTPdvBgW8+w4SAMB2gsqLltSnmWAHWZAmBJQkYowXYmXJDAkUAKLwxjkylZ4s5XiSpHW4Ca77iOIw/9Lprn8DSZE3UtJ5/B3/emRIP2rPF+7tR4gE0v/9Y5F88yJoB2jmSEqLRH+a+Wvkd+K3oXZ4oSxJkhe7peKsvSSC8uhWFl0drhL1UUM2TAx58dIoHrT4q9adRfGPC9Vniol5knhwgv1lUIyZKU5BplyChavJH70kyQFJ/FZIrBVVXqaxfV+HQ8c0zal44G9h5A5knD0y5Tb3fDsVcV+8JVDGvJISW6N59990444wzcO+99+K+++7Dtm3b0NvbixtuuAEDAwN44IEHXPtdeeWV2LFjB5555plpzyGEqUce9fw5HMup2+SKYro/9qmITXFnCqXdk4wk2AUTUkAhD2mu3JSC2q23XX3ClOfyGo0B5OFJ7d35sVCS4pg2YDqQQipxZ7TI5B0+uR1O1kTrlSvrXuO+G5+AviDKRK18xQNdQavNwRoH0tTP+8hq1rIJ2YloNW3Vqx2CLUgaSQvIQRVFmtaqRFYc24E5WqiSjwr0BVEo8QBaPnS86x6xigVJcjWfq5ceA+DqlGqOF1kDQEo+9O6oq8MxQMSsuWfdmjHWLt5DaOn7c0U8aDPA+Dt6MHLvS7CzZVb949WBOLYDfUHU1YuH6WLSJRR3TLBtlaaAq5SbEsbwCa2Y+ClZVDmmzcinHFRduiPvvag3kfLfBU8yAJLuiV+wqBpty5aJE21rqNKjppa8S5IEpeLZETymCfELiK2Ct1qKj+aobWE0v2+57/jmCtOZJnqjcI3cL4HDh3klIQAxK7v55psxODiI1atX47bbbsM555DW1ldddRX27NmDxx57jG0/OTmJrq4ufPvb38Y111wz7fEFCTmymEmfmMjadtbJcjoYwznktgy7XBhrtqk4YQJcCWEFdJXmDVM34uDKP0z9Igo1BMSwSSVCWIFTJJMUdSBVojpa/9SfgOz9yuNQAiqgSNUOprsnAcdxVRTw9uh0nLktQ2RSMW1IQRXRMxaQ607oiJ7WBXOiiOwzg4QsVFbPLDWQNVhZK71n9P6pySBarlyB7FPVUD1Pyii0zgibcPl76rLF99xPAJCbgzB2p6HEddZ8TQ6orpJSOaqj9cMrpoxwuFxx13Xgnx64G5//fOOVLWM/ep2QrrIFK1ctT6ZN4dSmIKSYhtLr7qgBn26oRwBYeoU7FgAYBwuQVMkVIVE7IijtmIBj2TXH4Qml1hlmDrXlA1kUKtb5PCRVRvw8t2mgd3yB3jiCxza5iINxME96xtgO0ct4iDvgFm5P9TcfPqEV+ZerbqeNNpFrFMbBfN1SY6D6++dhZcs1rQvmckwCM8O8k5CjEYKEzA5TPYzkkIrYWd11PwdqIygULodIv9DyeT2uEk86yVIHVPrgbLv6BNaq3e/hxF8HjXp4fRi84L04zHHiYQGjmrKAJEFSJGjtYQxbKZz4mXf4nnPfX/8WUkCF2hKqGoDJAGySfpJkCXbRRHBZEsn3LmPGWSzqkzEAONA6o5B02WX/7c1/81EHWspKJ1Oq4dB7Yq4upvQ+H/yOpwNqxRhrunA2HQdrQ287KO1KQVIklAdzxPtEk6slmiC9aSLrOlDYPuaKiMTOXchSUPz5RiYO4tgrTq17fi92/+PTaDq+qxrhkiVS2spQKa+Fu7qD9vupd82OQzxBJEV2EVjSk4WQC0ZEhnKQ4wHIulyjNVGTQQSWJV3XS1HvPvtt67d95JQOqE1Bpj1hWg76e9AVQJGgRDUEj2txOZxOSTrWtEHz6ePjJfX0dzCThch05wYaW1TwiJzcDnUK51aBw48ZkZAHHngAV1xxBQKBwPQbv4khSMjs0IgGZEYddSt9XOgqe6rQPn3Y2zkDUlgjLcQrZYVqR8TVQXOqlM/kpn4UXx+HlS2zFW7k9C7knqldOfEEpHwgC5RtQJchBxQ4VnUVqTbVr34BKvqPSoqFrqjtoonM4wM1JcX04V3sSzFPFBg2UKkuCJ/Q5ioF5b0ZHNOGXTThFEmZJu2Iqy+IIrA4gfJQjolA+VW9n4gvsDSJ2FndjAz5gVqe89+5Y9mwJkqkiVhFK8GnMgJLk6zbsDVZcpX88iZa/Op/Jg6mD3z623jnieeyY/CrfLtgEhGvRAis2hpm3VUlTUFoZQuS7yYiYtc1VRqx8b1Q6Hs19vDUkE5XIDcHXbbnSlRH8LjmGf/tNOxEuieNwKIYIEuEvDpgpdXURI3X+TRCLGc6ibN0j8eIzO8avJ5CXnidkOudywsR7Ti6MCMSoigKBgcH0d7+1vbeFyRk9ii8Po7y3pnV7ftFJfgHSHR9F+tF4fc5dSLNbyVhf96auuVPVyL7VFWUNt0DnkYWIus6WcibGZWtaWOag8RFvcg9N4zcc0Mo70sTQykJgCZD64iwfiShVa1o/sNjfM/5Hx/+R5yxbG3NyhoAJv63D4WXD5IVuAPIYUJmHNOGNVkmERcOkq6g6/PrWErEqyUBCAFwyjaZyKWqVoKP8AQWxRA4tgkH730Jjg1Yk9VoEN+N1w/8+L1iQMe0AdtBnusEy3uYuCpxPI3tlKjG0kv02mZCPJa09OCJ/+9hAKTqgXZ1ZSZcsgS1I8Js3tWmIDN/U5tDUJIBt57GclDur2o4vBGy8v4ME5BKqkzEmarMqoQAMKdUWgkSP38R62RMwTdu82K6iXT0B69WCQbALO6NoRwcwyYi6YoHiNLkb/Hvh5lGLvxQLyoyXcPC6a7ZL/XX6L4C84cZkRBZljE0NCRIiIAvpnp4NfoQmKrpHICa1TFAumSW9qZdPgR+OfrpIiks/cLZkjNL9vN7kKmYhNHj5p4bgp2uPujlBPGIoHn/wNJk3cmSVr+oTUFoC6IuF83s7wbhFAxXbxg5rsNOl1nkQFIqlS8qcdKMrOt0iQcpASkPZCCHNTglC1KgalEeWJpEuX/S11XWLpquah4/HUy9JoXeZmK2YcGolP3y4NNcU+kLDqWyZWAjEa5TTxiacmCRl8p3BRC/jeAxSSYQ5UtKC6+Ou8qO+c+rE6eD4o4JGMN5Up5K0xoRDUoyCCtdqrmPoVUtLPJU7/opYud015SPU5T2plGsaFVqmvXRa3TAUnCSLEHrCENfFEfyD5ZOTToqaZu5RubJARRe8SdYkqag6dJlDZGdemOn0TSBox8zJiHDw8Noa3trNwQSJGT2MEcLyL1Qv7ZfiWmInr7A9zP+gcL7Bfh9ri+IoHwgh8wT+9kELodJEzJgeh+Rmn4nlfJIP6t2vkojsrYd4z96g0xopYp4UJdJfxVNYWZaf3LfZ/GbLb/1vc59X3kckCRonREEehPMqKnUl2KTnRzVoTQFEVyWRHHHhMvZNLKuE1a2xCYeb3TCzhsoD2RZNIa2pteXJJC8eDGLkui9CZT7JxFYmkCpb7KqCwBc3hzAzKqWAKDUP0ks0yuW8XCI8ZTeHWVppOR7lkJfGPPdf7aVLfu+8gT0bjJ2qm+xJkvMd0ZJBmDnTVd6LrA4gdKeSXatVsGAOehurEd1RgAf+SANCs2JIhH30kdpSIXeFp5WyEwxk7RBvdV+qa/qGgsHzAOEVVRViFdkbQe5FkWuOQYARE7rhJqY23S7N7LFwziQhV0kjfv4ewxM7SXjBxHteHNixiTk3e9+97SakB//+MeHPLD5hCAhc4tGSuamin5491eTAZT2ZZB/cYRNstEN3ZAkCdHTu2DnDRbG9ppU+TVb4zFVSLq4awJOyYI5kifpFwDQZcTOWoj4hYtw8N6XYAzmsPBrG3yvM6Do2Hn9bwBFgr4gitiGbpS5yY7avmvtYeKyWnGg5LvkBle0wBzOo3yApLwoAUlc1IvJX+0hRl8HspB1hZSJLoq7dB7URp6PjPCvASC4vBnNf9RYGaU3tK52hGEOEw8Xc6JI0g5x3UXQ/IgeReKiXnz60592NbWcDvu+/Dgip3fB2J+FlTWYk6edM2CXiZV7YFkC5b0ZlzMn7W9iF0wYg1lGGuh+gI+HjENa1TtFC0oTITQ00gAJCK5ogT1ZclUL0euimKqiw5XSquiCpkJx54TL2tzPm4RGRALLkjX7H46IwXR/77Gzu2v657j2cRyAIx+hVS2+1T+AIB5vBcyYhHzgAx9AKDR1mOy73/3uIQ9sPiFIyOEFrxfgw8eSpjDjosRFvTWhfRrdIJ1qySrfMW1E1y9wfc5vT8EEcRNFmBPF6gqfI0ChFc3QF8aQe37YZelc3JWCOV4ggsV0pSurDUgxjVUM0ChCz9+e5XvNtKuqHFIRPLa55sGfeWIAckiBHFChd0eR3zbqcp0Mr+2AJEkwBrMoH8iyMt3sUwdg5QwYwzmU92fcq94KQVFbQ8g+NQBjpGrwpi+Iws4bcGwSQZJkCbFzFyJ0fGOukF4ypy2oRjigyDBH8+7Uz9409IqZm18p60B3DqtWrWro3ACw92tPQpZlaG0h0iG4bBPNBaoREH1JgkSLbAdysFoxEj1zAdMJeVM0AEnf8JGC8EmtmPix2wQRAMyxIimlVSXIqgIlrtctQa2bZqlMyHxX2XqInNqB3LPDcMomK3uloGTJj5TwY4qe0QWlTtO+2cAuW8hs9uk7w6FRosALUeuKoadISwm8OSE0IT4QJOTIoN6D2XEclLlup/riBBIXLsLB+192hZdJHp+Us9YjIOw9x2HpFqCaj7fSJWR/N8T24UPHueeGiLhPksjqzEG1O6smQ2sPQ1JllA9ksTc7hA3/8H7f62EEJKBAbQnVRF+oGNYpEjEkrciQY7or0pF9cgD5V0bhWDaCy6u9LEp9KWKtXSm1tQsms6N3dWcF0T5Qfwk+GtTIREHJo8sfpCsKYzDLjkOreQDS4TS6vsvXeps21+v885OnPS/Fzz/9XZzQuhxKPAAlqrlKqANLk7CLxMit1JeCnTPgOETUahctQJeBogW7ZNaU21IreyVR7T1EHWq90BfFiT35QIYdh68o4VMIdd03PZE/P1AnUStnIPsUueeO6ZAmeRUoyQDCq1phFy32G6IILElCbQ4itmGBKyJzqJg2qnkIzqJ+1VjezrlC6/HWg6iO8YEgIYcXDZlO2Q7L01PRKN/mXG0OIrSylQnnvASkngLfe76Jn+6EMZRzCQ1d/S8AYuQlSUQDorjJQW7LELpvOL3ute678QnAtKEtjEGSJQSWJtmDevw/XndFPNg5VRlNly1H5OTq31n6N3uRfZaUCYfXtDPDtcL2MZjjlf4hjgM5qAEy6Q1ipYrEzrsjAnO0AEnyE1ROv1LNPnMApb0ZUvZcAa0AosfgyQcAtF1zIiRZ8vVcmapc2Yv3rHgH7rnim4BCoh7WRAkOiCEZRfDYJCZ/uYfcvokSEWA6DiRdIdERy4GVr0bUKInxpoVoWa0XrVethhxQMPbvr6HwWjUtoHVFEVyWZBUj9XqdTFf1wRuP0bHwEzFNrUiqzCZg/r7z6LxuXd3uujOFmSoi96x/tQngb4Y2ExR3pVxOsfxxg8c3u4SrgcVxV7muSMO8dTDnkZCBgQF0d09tSnW0Q5CQw4fp0iX8Z/S9wvZRWJNl5iKpdUUgSRLrH0JXrN5V03Tlf95mY1STQaMdSiJAWpNny+Q9jUwC4TXtTF9Rb0L9ySfvwbqOVYSALIhBietovXKl2+E0Z5BeLDIAjUyYanMQrVetYiFnr128pCkIrWqFnSujuGOCtEo3HUBzNwujXX+tTJl0rkUlWpArM7t5SZUQP29R3e8q9fPdpPy4AklXoCQCrpUo7ZsCEC8S2m2U9pKxCyYkXUHnZxqPeAAV8gYSqdB746wKyavPyD0/TBrpVUqWJV2BVGkPb6VLgOlAbQ1C0hRXtCPzxADsgulLPAJLE4id28NMvw78v9/VRE9iZ3Yjds7CWkEu/U35mL0BpFlc7JyFrvfyLx1EqT9dTWdVYE2WyG+QSiQqTQDN8SJKu8l5lEQAkizVWPjPBrM1ApuLc8TP66lpuOfdnk+jzeWYBOYXMyIhmzdvxoYNG6CqtUx7aGgI3/zmN3H//fejUCj47P3mgSAhc4/cCyOujp/04eFdPSYu6nVV2FBTJWo8xq/eM08NoFDJjTsO4BTNugZYXhgjeWjtYWKalTOqFuYZA9rCKNOc2JkyM3KKnbXQZVBWj4DQ9AtMG0oiCLU1xLQuVrqMwutjcDIVq3SFNPySA0rNOO2CydrZSypJ/wSWJlF8fRzGwTzzJqEeIq1XrUbmt4RIeXPqjTaTcxwHB+99yfWe3hND+MQ2FF4dJ9tYNgovHXR1Oubvc6kvBcey0fmZtb7nqId9Nz4BSSE9b4LLm6tpnsVxQJJQ2j0JOaTCGMoxa3UarZIrxChyWidKni6tWkUETKtKvMSDlkjTpm4AKXsde/BVAFU/Ea09jI7PnFzXxG0qR10vvNEONpbuGIqvjzNxLVDteFvqS9VUkMyWfPg1ruMxV11j67kgA40TCD5lSvfjyYnWEUb4xLd2xeZbGTMiIalUCp/5zGfwyCOPQNM0XH/99fiLv/gL3HTTTbj11luxatUqfOELX8CHPvShwznmww5BQuYWjUQ/qCiUf6/wyijskgnHsNkEHFrTisKLozX9XAAywcNx2OSoNgVrbN4jp3ZATQZZlQirDilaQMU63M6UIekKnLIFpSUEp2y5zMQ2HHcqnnrjOd9r3ffVJwHbBiwHckxH6IQ2l4125on91TSPSiprzPEC4AClPZOulAbvrSGHVCJgdIjVN2zieBpc2QI1HkBwWQLFXZMunUepLwUlGUTiXYuR+737Ie73HXknxbarT0B5fwaTv9oDgEzGjmFDjmisZJiSD7qSPW3lWjz76gu+98b3fv31byFHdMgxjd0nu2TBzhs1lR50DOTm2JBjOvSeOLT2sG9Eg2/H7lg2MymTNBl6D/m75lfgjmkj/X/7UNg+BrtgsHNR6/ipuuAC0zuXTtU+nn5fPLQFUSTftRjpx/a7dTjdMTS9d2ndY9U7/1SYy4hC4ZVRV9UXhdoUQOSU+mZ304G/hvBJbVBiuqt6SERF3pyYEQn59Kc/jf/5n//BFVdcgV/+8pd49dVX8c53vhPFYhFf/epXce655x7OsR4xCBIyNzCGci4V/1Rlmfx7xR0TsLMGrFy5Ysol16y0+c6cUkCB3l1tB+6tAOA7x5b3ZVwVEbZhQ9Zk4t4JiYkb7aLp8sqYzreiKZzAK1/5FWsGJ4dUdHzmZJa6YCH9sg3IgLYwBkgg6Z7KZMeLLI2DeZhDOdhlC0oyCEkilQjmaIGIcpPEQyR2djcyjw/UpJYcyyb/r6RlvN8BvS/0ngBVV9Pg8S0wx4vMQZT2PVFiusv7gtqo//pXm3DRuy72vS9+oKkWgDiHQpVqxIzUTRUA5LBG0k5wd5ClKTaekCqJAALLkqQBG0c8eLIQP7/HVf0yuakfjmWjtCcNK1XVHkkhrabBHC3rnW7Cs9JlTP66n6XCvAgsTYA2yXH1RuolImzHdpDZ7CYfjQqIc1uGiVC5Dnj7+7lC3TTLIQhV/WCXTGR+6yYeU2nMBI5+zIiE9Pb24jvf+Q4uvPBC9PX14ZhjjsFnP/tZ3H777YdxiEcegoQcOvgHA7WkTj+6F45V/bnFzl2I0e++4trPyhpwDMs3pcK6kVZQ4+JZp0me1xWVEgW1OVQVdVrEHRRSteMtPUfiol7Ylg1Frc3xA8DQXS/ASpVgZwyo7WHIQYWFyUfufrFyzjJggXTWtRxGcCiZWnD9egBA5rf7Ufj/2zvv8Kiq9I9/753e0kkjBQICoQgSBAEVdEXsYAMbioqK2MCfurIiCqiIhXXdFUEXBTvYWHVRzEoTsACKIqFIbwkhIckk0++95/fHmXtm7pQ0AqGcz/PkIXPnlnMnw5zvvOd9v+/myuhurqDdP0lAiRJk4a9HZM8XVrUR/Buoz7k3lLMcG1VgmAqSWC6H+rcwZFhhyLDBv79Wkw/iD/iRfnmnmK9HLH5+4ktkkZD5nOgwsmU2xSNBMFD3V1VwqSg+GeYuKVGVKmolDgCIFgNEs47lwvj3OqPeG5G26OrroPYJovb4hL4PgmXR6mvf2CWPeNEOxRWAIccRFUnx7azWROri9eupT3zUt9yhciwmZSITOJce3TLL0RDL2JCLkZOTJokQg8GAPXv2IDub+jJYrVb8/PPP6N69+zEbYGvARUjzUTySpqlZ4pD8qHJHY7vE6NB5u0S4fz0E0aKHdMQLY7YduhQzHOfmwJhlQ9VXOxAIupaqCYbh1GvJvrsGUqWHfaNWk/nkah90SSbaVbbOH9ZLg1aWqJPG1j+24Px/3RDzfis+2gy52odAhQeGVAsgAG3G9EDpi2vpxKYQmjhqpN+8Bb1InVLbJVIjrYiOp8xu/aALxmwbTAVJbFkKAEy5CUi4pB2qPtnGjgmfpOp+LoVc449Iyg0lj4Yv8eiTzRCMOhhzHNC3sUA67GFjCO/CC0IgVfsgV3mbVNnyyEV346EBt4aWnwSaA6OiJtKG5zkYMmwQbQbm9RFeWaO4JYhWvSYKBtCyWUEUNEnJQPS38CMLt7JjpSovoNCyY1b9RELisDHCw7W2DK5foqtH4jmlAjQKE+kHEkt8iGY9DNn2RrurqrS0D0g46nsrkpbKH2kqkUIoVqQ1ljEa58SiySW6ZWVlzLbd4XDg999/R/v27Y/ZAFsDLkKaR6wPyKh17rZ2BA7Uhb6hX5AL57J9zNtB9kowpFqiLMZVGkqwdC7bCyLRt7Rnc6Umt4AEFEAnwNwxOZg8SSBVB91CzToYUqiHR+2q/bSyQQfk/K1/3Pste30DBCG6GysQzF1QS3rtRpZYa+meBsfAtiyiY8xLYMslqnBQy11NBUnw7qiitucALF1TEQhba9c5jEi9qZA9lqq9OLKATrSqX0h48zkgFFVS/SPcG8oRCBMfukQT69mhvu5NER6ANjEXAHO/FO1avwp9shmGtnZWCWTIsNLeKwA8m2hCbnDFQtNJGAB0CUbo06JbxqvCI1DhgTuYDB1ueR9uTS+YddAnmCHX+mDtngbBpI/ZTFGFEIIjC7exZSoVqcoLXYIJ5jOSo8cTFoGpbxmSLacFIyOJQ/JZjkp9HOtv+/V5nTTVUv9YoUlSTbfA2jMd7t8Ps/cSwKMiJzJHZdv+5Zdf4sILL4TNpl1f5LbtpydRnW2D6+dAjIz24IdFZAlq5DfIeAIk3jdExeWHb2+tRnyokRNNc6+w6IcuwQRBJ2grawjQ9m+x/T++uPMNnNW2q3ajX4GYaASRCUjQ8huApmw23j2pr034t35T+0T2LZt4ZegzbZplCkvXNNaQTKVuXSmIV6Y5Iwkm6KwGKD4p5uvmWlsGqdrHTNx0yWbmA9JUEzGACjK50gMiAsQlBQMv2qUN4pVh65sZVbqq3r8SkOH6qZS9boC20Z0x1wH/vtooIWrrnwXXD6XssbokoyJVeVk/lfD3WWTScuxo2u4oLwv1HObOKVFRh1g5EJETufXMNNZWIDKRuD4/kXhlrC0JCShwLo8tfE70ibxes8KI7ZwThyaJkNtvv71R+3Hb9tOXyPbj8RLHAuVuuH87rOmPok+m5ay6BCpyfTuroU+3Qip3R+U2AGDfdlVjMyLRSIf6Dc1+TjasPdtElZ1KVV4oNX7qzxE2SSoeCaLNAGvXVCRf2THm/R2Y/iNdYhEFKji8Ei2V1QvBvBIE/xVhyLCykk/VwySWS2nVoj8ROORmAsQ2MBs1X+1kCausd4xRB3P3tKhvoL6d1dRmPmhSZsqL9qhgyzWrD0B2S5Dr/LStuz+UGNtu0rkIyFphUx+HZm+ALskMT0mYhXhY5Y9o1kO06mHulAxBH3s85XN+Q+CIh1Ynhd2ragZH/DL8+2vZa6ZWwYQndoa/DgDYeyZ8mUd2Up+ZyGZ/gLZZolTpwZGwpS4gOooUTrzEy4aiGN4/j0B2+jXJyJEcrwnT+b89iDULmDslw5R/cn3+hX/WCAYRCYNzo7ab2ifC3DHpeA+NE4cmiZDTBS5Cmkc84yYVU0ESDG0s1OMCdEIOBHuyAOHdYAkIQciErCAJpnYJLNwdGcKO7HAqCEDCRaFvQmqEQZdiRmCPE5BB5y9jyOCLyASCTsAl02/Gr3s2xby/A9N/hM5hBAGgOP00kqITIJr0dAwGkeYYCIJmeUZnM1CjrxQL9ElGAIJmEgboRGfukgr3L4eAYMIoTDqIRh2L1IR7pIS/1ixB026EpXPIzl3dFwCcy/eBBBRqkuaRIBhECHoRC374Ag9/8VzM+41F9be76fVkwpq8QQEdc1DQERCIOh2sZ2lNDROH5LMJz7W+DEQhIL6Q+LCdlY6Ei9uh+r87EThQxzrw1jdRy7V+6BxGbQ8ik56Zl+lSLZArPexYa880uH/TiuSKd0tY9Q0QEh2iWQ9LtzTN9RpahpBrfKgLK4dWCa/gEW2hcuRYdu/Hg1O9E22sqIhc60fdj6VR2zmtCxchMeAipHmEEkGd1CsjSKylCGbDHowqqAmBos3AvvmqCaThzqjhiZU6uxFynZ/tF34t385qKB6JLVkQvwLiocsEYoIB+lQLFK8M0axDoMwFwaSLa7+emZKO3577FoqXlshSZzQS+rZvN0CpC7CyXtXCG6BdVdWJNjwK4v6tHHJtKMnPmG2Hf7eTRlIIICYYYUizwpifEDe0HCitg1zjg+wKQLToYelKJ0xdghH2fjSvoeKDzfDvdYZyNEQB1b5a9Hjxsvr+lBp2zV0LYzm9B7WyKJzwSFJ4HxWA+jmoHWNVMUgkhfqNmPQwd06GLsEEa682ODx3o+a8kZEHY54Dls4pMStIdIkmVtWjvl8C+2pZ0zx9moWZ5fl214D4Zba0Ef6esnRN0wjIxooD385qeHdQ0SzX+hEod2uWz8LzWUSLAWm3do11mmNGZMJ4OKfqZBxvKYYv0ZxYcBESAy5Cmkd4d1wAmo6XzCZbUuApqYTs9NEKgHQrjHkJmvJbtWokvG9MOPpkMxMQbFsbK/NkUPcnCgFxBUKN5whY7xc25lqaF1Jv91t3cAInoCJBAa12CZaYQia06iXLBkuPNtSOPUh4vgcAlusRbgOOgELPqaNjdAzKBURBkzsQjs5hgFwbYBGQ8GRTiAIOv/UHAoeCCaxh/W9yp50X8x5j8drtz+K6fpez11NRBVPY8hUQXMIy62E+I5lWLBFCo0phybbqOUhAYctT+mQzoNCIV3jiKEAjYjq7Afb+2Wyba/0h2ik46GmiEiuXgvhllosE0GaFFe/Ejm6FN0EEmj4hqSXVKmoFj4pU5dUsAR3PCS9etONY+IScyDSlVQTn+MNFSAy4CGke8T701IlIdgVo8qNCowjGLDtMHaKFhq0oM6oxl6AToUsISwIktBok0ntBqvKC+BWaaOqRaHmseg47NZ8CACIRkICM7Uf24oJ/3RRz3PsmrqTigJ0g+K8qRIL/ClZqoGVslwjvn0fYN+fIypTwZSNBJ1JR5gvmlBAApuByhpdW64QTHhXwbjsCIilBbwtoUiPCHUUBIPe582PeWyzaJKTijxe+C5XE+mQa0ZEJXXYy06Urf2mdxkQOAHTJ5tD9hhmdAdCYw4k2A/NkCV8CCXekVZFr/cw6PRxTQRJsRRnMhj0W7l8O0fLrsA7CglkHQRCOShR4SirhP1AXtdSoJjSHJ0E31k21JTnVl1maSzzBEemzcjySfzlauAiJARchLUP4f/Dw7rSiRY/sx/vBs6kS/oN1rE254pfY0oWKOvlGCpVI8SHX+jXLG/Cp5aEADAJEq0EjChSPFDf6AVA7cahDCeaP0F8IneANOtq1NqyKI974ZKefOpeadJCPeOlyhqSExIcAmtgqCpqlDfW1ohsIXQqJFEXq56W63SAid1r8+4p5r6qDadAKXakNNuxThRYJ3r9E6DilUP4HK39WCFsOAagTLPHLtDswoU6zYoIRBAR6u7YTbOQEGW5Ip8JM4+IsK0g1Pvi2h3qhEL8SaniYYWP5RE2djBvKczK2tUMwqZEPAiKRuA61xwLZ6UfdT6UxnzvdhUcs4kVFalcfoBHPGM9xji1chMSAi5CjJ/w/u3tDOeQ6KhAsXVKRcl2nYKKkDN/OGsh1fogmvSaMnX5Pz5gOlOEdYgFEiRMx0QSpLLQUYRvQFoH9tVH23vHyP769/x0UJrQLTsACoKfCQHFLEMw6EJ8MfZIJik/WJEyqdu+Adu05loOmdMQL4pep4IrofgtQJ9naFbQRnfvXQyAKoV1kVaGhRj6MIo1I6AS0nRTfzyQWqvAQBAEkKKaUWr9W5ASXryAEK38AQAz5nmiWlFQUQn/U5a/g/RGfzK4DUFdatUkbUQhtGGjWa6I6uiQTzB2oePAfqI0SqMzzI6wiRx2DaKPntvbOaHTCp293DR17DKQqL3QOIwS9SIWGTgiNNSIaBcROom0IQ6YNxjwH9BFGfJHEi3aofZE49VPfMgxfojn+cBESAy5Cjo7Iyg01VM3C4MEW7CrqZO64MI8mZ0L7jVOq8sJ2VgZzxGRVMTKB7PQxXw3FI1GDMo8E0aCDrV8WfDurYciywX/QBUGg3XNzJg+IOe59T3xPJ1sC+o0/uAQRPuEas+31+p+oH1pHPtkGqdKjSUiUgktR6jKRmGAERAH6JFOUDXvgkCtkcS8RCEbqZyJaad8UKAqemPE0Xlv2TiP/KrSkVu0Yy8pZM2zwbCgPCZFgdY86kas5H4Ke9qMxd0rR9EMhCoHs9EM06yHX+kECVCgIBhH6NIumugUAK8GOlesD0N4s+lQL8/kI30fxSBBEgfW4CZ1UhDHbDqnSQytjgmOI1XAOAASjDoZse5RrbySRTeXC/5b05tEi4qMxxGt+d6yudyKicxhgbOuAIdum6f3TXOJFRSKfs3RNhbGt/aivx4kNFyEx4CKkeUS23A7P64jZHZbQXAJzhyT2nOoQqkZG1A9ZucpLjxNFmNolwLezmlmOOwZmo+zVXwDQicrcKQWGdGtIrAQTIi94+nqUlP0Zc+z7Hl/JVltg00PUiYBAqyU8JRXU3TPHwUorbX0yoE82w7e7Bt5g6/jEIfmQjnjhWn+I3butKJNOuEdC/WPoEpEIW98MBA7QqI1ajsqWQEArhQSdCGN+Arvulh9/xzmTr2r03+TAa+ug1+k1TegAQAnIkA57Qss/Tn9wWUgMRjMA0WGI+tupmAqSYOmSArkugKr/hF5TwaCL2Vbd1jcTtSv3w1tSiciPnFj+G+oSnVzro0LIpAdAoLgkGp0y0/wSS2Eq2z98bJHU18EW0Hbcjdw/UnzoEoy0Y3MY8cSAIdMGS/fUJpffBg67WVVRJM39di67AggcrIP/QB11D+bAv8fJlu2Aev6ObSyw9kqP+Rzn6OAiJAZchDQP9dtDoMwF2eWnTd08EvRJZrbU4j9YRwWGRQ9L9zTNEkn4B736YRDeTTXWY0thCireKwFABYjj3ByN86hU5YPiCcTN/+iYmodld78HwWoAZIWW++pFCAaRltJuPAydzQBCCFsaUCeB8PyE8CqYwBEPBAWAmhwL0O656v80vQBjrkMzDqnKS0Ppgvb+AWqIJTbhm9+KFSvQ00fH6N12RJMro4TnzaifvUZRU0WjdiRWX0Nj+0TNa24+IwmeLUfg3lAOAMwlVn3tVYgarZAJW45TiRQe+jQLbGelo3zObzFza2SnH7oEY1QeSazwueKVNC3eYxFvImfOux6JiU8VQ64DgRjVOS1FPKEULn7rw9wxCab2iS02ntOJmuI9dNnTHYAxxw65Wvt+PZFs6k81Wl2EzJo1Cy+++CJKS0vRrVs3vPLKKzjvvNilhKNHj8b8+fOjtnft2hWbNtESvDfffBPvvPMO/viDdmctKirCc889h759+zZ6TFyENJ+a4j3wbKqg3+p1As3dEADRpGdN2ABtwmk4ai5IJAkX5Wmy2E0FiahZspuVd4ZbnSseKWxZRUTu1IExx1r6j/VQ3AEQnwxdghFStY/5lehTzKF26DoBpnz64R6ZVS8d8dLOs8FxqCW/hgwbLZNVxYcOdDkpzBNFtSGn95PEzq/ef9LF7Rp+wYMMHToU33zzDTvWv78WgUMu6JPN1BnVF0wSDSihZQRV14gCTa5UCESHATorjYDoksysyoXZuhPAXxrqv6Ius4WLSYDm5ig1tAxbtOhZY7pYYW/vn1VRZbrxGsDFWr9v0O68Ee3k1XNJVV7IVV7N+ez9s1D3gzb5s6VyBWqK90Cpo74i4ZzoyyynYpmve2MFAmWh3kw8H+T40KoiZMGCBRg1ahRmzZqFgQMHYs6cOfj3v/+NkpIS5OXlRe1fU1MDj8fDHkuShJ49e+KBBx7A008/DQC4+eabMXDgQAwYMABmsxkvvPACPvvsM2zatAlt20a3eY8FFyHNo/qbXXD9coglEAo6AYJRx5ZD9ElmGHNpPoVvZ7WmeRt1UvVozhfenTNy/fbAtB9obgDAvoGH9wuBIGBL5S4MmX1rzLEemP4j+12XaEKgzMXEQaQ4ihfel10BmmDqpUmXIIBo0oWcRNUKGIDml9gNsBVlwr/XSat10iyaeyIKaVLEAwBb2lD8MmpX7Id3RzUVDkYdlMOe6LwFo0i/0QnBvI1UCwLlbvZaAmE28UHhKBh10NkMUaW2mQ/0jpt8G/66hYuAwGE3qj6jyzdyjS8ULQEVPRljewKInyAYqPCg6lOtrXr43yfSX6Q+wq3Vw43kVGx9M+GKcD892onJt9cJ79aqmM8dj0nPu70avrCO1icDtr6ZDSbrtiTh773wNhGcY0OripB+/fqhd+/eeP3119m2wsJCDB8+HNOnT2/w+EWLFuGaa67Brl27kJ8f+z+wLMtITk7Gv/71L9x6a+wJKRIuQprH/qdWAwhNYqaCRMhVoW+48aIckUR+29WE+P0yAkHnS0EvwpBupdUmPpkmJAYb0mU/cnbc8x+Y/qOmpFZ1+tTZjdCnW0MTOaCpgFFxrS+D4gpQgSUpEEQRgomKBzoOhUZigsscqjlaZN8SXYIRxlwHTG21SzMNEflftnLBFvh21tC8jlj/m0VAsBkg6ARtbs4RL63qCSsztp2dCanSG8qnIQSBUpfGoMzaKx3+PdoGcZGvk7VnGxjSrVF9e9T9ASpyLN3ToE8xw1aUAaDhVvWxmv81FanGx8RFpPiw982EElBoT6IwjkYgxLsnx6CcRi2znIwQQuD5o1ITWTgZULtL+/Y44d0WEos8KnLs0De8y7HB7/dj/fr1ePzxxzXbL774YqxZs6ZR55g7dy4uuuiiuAIEANxuNwKBAFJSUuLu4/P54POFJkun0xl3X058wiMJ9r6ZqPu5DPrk0Lf9+iYYNRLg/G5vTFtuU0ES6n4qBQlQN1VdqhnmDsl0HwEgsgIhWCIbT4CseH4RuiS1AwDWNE9xBSDaDLTKo84P377Q316fbAZEAaZ2idTR9c3f6eRLCKATIYgC9Fl2EL8M+YiXlvAGFPq8UaSW4ZIC2elnSW1ytReizYgbp92Nb378X6Nf2+pvd7PfVR8N/75aei05xgHG4DJYsPzXmJdAS2UDSqgyRaB/M8FmgDGDhtalSioQ1KUiQRCClSde6FOpcHNvKGe5LoY0C/TJZgh6Eab8BDj+kofDb/weuzQ56B6qfqd1nNeWlTXXrj4A/4E61sk3VqKqLlhFpHMYYD+ncdGOcLw7quHbWQMiK0xEhS+D+Q/URfV9ae7kc7qbhgmCAGuPNKBHWsM7HyVEJnCtLYVcG2h45wYId3wOx72hnCemHiNaTYRUVFRAlmVkZGRotmdkZKCsLLoBVCSlpaX4+uuv8cEHH9S73+OPP462bdvioosuirvP9OnTMWXKlMYNnBOX9Ht6st9ZbsKeGhjzo5PlaHUBYR1zwz+0pXI3S2Q0FSTBdnYGymf/xkovbX2zINf42GSquINCQlKQ82Ts8lvXxnJUf7WTfvt3B6hjZ60fxrwEWjkiCpBr/TDmOKC4Aho/Etf6Mhr9UJM6RQGm9okw5tAIhmt9GQghILV+iA4jiEJgPzsTrvWHqB9GAm2wtsGzA0MnXNvo1/PQ7A1sDKG+K9TplVm9q+gA6EXoE00gMtF8YKrN+dQGdgCdJHRhpcEqlm6pqP5yB/07BAUBjeBUQ/GFSl9NRXTJihBA8cpQPF4EDrtRt05bEdXm7jNZLo8qPsKTShWvhMDBUI6JMTfUAThxSD6ITOBcujeusVljUJv3+XbVAISaiYWfz7e7RvP+E816OM5r3NKtindbFXx7or+8iFY9HAObdi5O0xB0QrNEaWOJTIbntCytJkJUIv+4jf2Dz5s3D0lJSRg+fHjcfV544QV8+OGHWL58Oczm+CY+EydOxMMPP8weO51O5ObmNjx4ThQkIMO5fD+kw24QicCYnxjTcExjwQ7A0iUFxlwHaor3QJ9uhT7disQh+Tj4/E+oXUWNu/SpZlgKtRU1ukQTiF/BwBevw+4j+2OOqey1X1H91c6gzTlhORKOwbmQXRIVHAEZ7t8Pw7+/lpbehvlYqL1jBIdBY/sdKHNpKk9EhxGKNwAQAbXL9wF6EUSR610aimTNlP8g35hBk0LrAszQi1m/qwIkLLlUdBgh2owwdUyEqKcTeHiypqATINf64PmjkvqN2I0wh3XbTRySD/fvh1G7+qCmrNpWlAnvjiq41pdBn2yGaNLB0iUFvl017G8gCNQOXTTrQBQCQ5oVuiQTiE+G/0AtW4oJr26hEz6Bb2coN8HSIw2OAdrJOlwYmDskwVTQtMqPyIiaPtkMXbKZNfjzbDmiuYY+2QRbn8xYp6r3/JEkXJjbIj4WnBMDLkCOLa0mQtLS0qDT6aKiHuXl5VHRkUgIIXjrrbcwatQoGI3GmPu89NJLeO655/C///0PZ555Zr3nM5lMMJmOX+LTqUpN8R7ItX6NmVWshL9Y1QpyjS+q2iE8+dTY1gEQwp4jAQVSlReBfbXInR67P0q3nE5Y+sRC2uvEoKMGY4ROlKYOSfDuqIIgCJAQsnIXzfqgqRg9B1EUWl4cnPTDTcX8B+uoIAAACFD8fpYH0pSeLeOuuRPPjX0SxC/DvZF6Q8jVXpg7p0Aqd9P271Y9pFJ3yMvESJ1IdQ4jzJ2ooJAqPQjU+GAqSGLjDBysY9UsgpEmoqrLSwBweO5GHHz+JzYWwaCDpUcavFuOBP929O+k5n1EJjVG5mU4l++D4qcCJPw4VXSGl08DgLFdIpKGttOcM7IRYnOt1tX3nmoupyYZujeUawSEIdNGlw4aQF0ujMXpsszC4bQ0rSZCjEYjioqKUFxcjKuvvpptLy4uxrBhw+o9dsWKFdi+fTvuvPPOmM+/+OKLeOaZZ7BkyRL06dOnRcfNiU9kxMOQZUfyVR0aPK6meA8CZS5ao59Pl0f8weiHoBNZtYN6fiYA/Apyn4892Vd/uxtQCFy/Bp1ZFQVEpq6gcq2fmp0J1MdDOuxmIkPxShorc+JToEs0QzTSEL5nUwU8myq0vV90APQCcqc2vkutOkaNKVallyXMilYDEyBKjZ8mnQJ0KSgYuVH/9e2shr6NFfpUC3UbPVALY1tHlCtp9uP92Osd6cch2gywdEqGd5cT7l8OgfgVSLICQ7o1yr8lVplt5N9etBlgyLDBhFDuh+rFEH4u9XiV8AiOagjXWGqK90BxB1gypKl9IiAIbLx1P5ZqIlemdgmsp0w83L+VI1DuidrOzas4nJbhhCjRnT17Nvr374833ngDb775JjZt2oT8/HxMnDgRBw4cwDvvaK2pR40ahT///BM//vhj1DlfeOEFPPnkk/jggw8wcGDIH8Jut8Nub5z1Lq+OaR7qZNLYb4WyO4DKd0vYY1NBErN5h0xiG3oFfS827t6MS+eNiXneigVbECitg1TuDvUwEcF6iwgiLR2GACg16uQeXE7xSDBk2miOSHAJQR0by0Hx0OUZiAJyn2ma8Dgw/UcYMmwsn4S9FnV+JjoEQYDilUAUAH6Z+XnYz20L/15tHxx1wvbvddJEWIBGjHbVhMzG2iWyyFOkMKEOqgJkpw+KV2Kvj+oBYSpIgrVXGxjaWOmpg8ttKlEN3fITkHRJe822hvpx1BTvYfevovHpGJANXbAXTCwiRVBk/oiaE6Ji7pwMU178/9dxl1ka4TfC4XCaRqvmhIwcORKVlZWYOnUqSktL0b17dyxevJhVu5SWlmLvXm34s6amBp9++in+8Y9/xDznrFmz4Pf7cd1112m2P/XUU8xLhHNsaKz4CJ80iEQjFCSgsNwPgE5man+Q8KoK16+HkPN0bPMxgHa/ZZEKgK4mCIBoNdCEVL3IetAotXT5RDTrkXprV3hLjmgmM1WA6NtY4VpfBtFqAAko6PfKNTjoLEdj2Td5laZySEXjslrhBvHTMYsmHe1ACwBGWoZsyk+Efy9d4lCjBb7dNSAKgSAKTID4dlbD1D4RstMPQRQBQYAgCkx8iGZaIUN7wRCNSVZ4f5/w5NFY9uFsqSMocGL97ZvSDExnN0JnN8IxKAeCQdQY09Wtia5YCH/tVEwFSbB0S2WvdeT14xlsEVmBc+m+mOPiyywczrGl1R1TT0R4JKTlCZ8wwr+JmzulwLvtSKjkM8PGzIHUZQnRpGOP43W/XTFhAQps2azpmjHbDv9hN+CRAF2oXFXxBrvgBr/16xJN2m+3okANxzwS9Bk2QCEIlNXhsxX/xbiFTzb6fg9M/xEQaHM6lbTbutFGbzU+VC/eBanGy6ztQYI9Saq8gJ4KI+KXtZOmKAKE0CZwjuhcKN/OashOP4is0AqWdonw7qyBXOOl1TsuibrY6kTWL8OYbQcEAel3nxnV+ycS1XQunFiTtPfPKvh2hypF4kUQPJsqQ51w45xLpe6nUtavhRACf1huSuQSUaT4sBVlQJ+iXdapXXUgZhfgxizRcDicloOLkBhwEXL0xMoTUMWHzmGkzefa2uH+/TCbDHQJJujsBrafmg+gdsuNJ0BU91N9shmBQ246wUoKWBanniZkWgpTNV19RaOOtXwHgJQbugCSgtrVB+Hf60T1gQp0ef7iRt/zxklLkGJLhM5uhLF9IhSnD/o0uoyROCQf1d/uhj+4TAKEOvMKBpowSySFCqVg6bAKIQSCKEb1BUm4MBc1/9vLusGq1UJyDe1cy5rmAcGlKAGiRUeXaNo6INV4YUiPb70drz9L+HPhKD4ZtStD0SzrmWkwZMQ+v8aVspF9OdwbyqNcdesTH/Z+WZoqrNPdu4PDORHhIiQGXIQ0j5riPZBrfJAqoxP51GUDgH5zdf9+GFAISLBpnC4YwQBoQqFahSFVeXH288NwsOZQzGvun7qGVdAIBpGu/QcUQC9S8zKiQNCJGodUFeuZbdhyBUTavt63uwYZY3s1+p6fvez/cGufq2mlStB2PHyys52ThSMfbNZeWyHULv2IB8QrAzKhY/fLEB1GNtZY/VP0SSZI1dRYz7ezmpqs1fio1kox08hCuAW7wwgQQLDooVOdUdMszJ9FxZhth6VbqmZb5KRtzLGzrrWRNHbpxfndXk1yamMEQEMiKPJ5x7ltqZiLEEWNGR+Hwzm+tLpPCOfUgSVLtksERAEJf8mDa10Z5JpQRULikHyUzwkZj+mSTBAEgYXl9clmFnavb/mlKKc7Ft06C8QrUYMwn0yXGbwSBKsBxBMABBpBUCMqhhwHfH9WMRdR/75aNsk3pVkcQKMvakTFVpQZFTVwbygHkUPmYEQi0NkNMGTZIVd74T9YR5c2/ApgECGYdBCCy06mgiTEKxgPVHjg/q089FrVBBvn1fnhdwZLhIMJuDqHUbNsY2xrp43qUP8kHDmpJwzOjVqGibdvY8/bHPER7rAa8/lBOahdsZ91Ng5H9aHhcDgnFjwSEgMeCWkeUo1P02gqctKp+XY3q9ogAYUtPwB0QjXmJ8C/x8miJvEiEvv+tpL+ItCmcJAJoBNopUtwrhTtRoiJRljOSIFvZzUUSYFU7mYCxFSQ1GThsf+p1RDMOk2kQnWJJQqhDfx+ot1WWa8VmeZwhFfXEEmh+RnBih3BqIOlayp09qBgIIS6gIHmYfiDVvKEAFBIqOOsTqTLLVLQvMwQ9A6xGSEYQ6Ih8bL2MOU2/D5urqBoyX3lOn+DHWujIiMKYcnGjb0Oh8M5MeCREE6LoQqQQIVH0wAs4S95OPj8T7S5m0K7zQp6OmEKooCsx/pqJpZft2/EpTNjNxvc97eVbMI1ZttZgzX4FCZA9G2ssHRLAxRFU5JqzLY3aakFAA6+tBay00fLek06FlWxFWXCfk4WAGhM1USTHhBDrehVW3LX2lIQASB1UnDSpEJJdegMlLmgsxuh+GUE9tey6+uCia0snybBRO3T/XLINVVPXws1MsO61zYi10Kq9MD1S+ObtTVFUETu35Tzxtpf3Ud9jVQfkHABwoUHh3NywSMhMeCRkOYTOZlovDWCk6ZaQhneVde7vQpyTfzkUwDY9/hKCDYDSECm3XOdPppT4VdYVMGYbYe5YzJ0DiMzKvvHN3Px3KJ/Nvoeqr/dDcUrwbOpAkqtH4JJD9FugLVHm9B97aqmiZ9hFRZq8mv4fQMA8cps+QmiCIiA49wc+HZWw9DWgcCBkOiIRJPESmgvEsUtATLNe7H1zYJc4YEhO+SB0xJ5FpFEem00RXzUt39U3kmuA5YuKVH7aEtxE6E6uVrPSochzQIOh3NywkVIDLgIaR6RE4qnpBKKh3a2VL+l65PNSL2xCyo/3ML2U5c24kUpVt73Ido72kKw6Kn1eHA5RPFIgE+BmESXMZKvPgOWzimoKd6D3eu3otfEoY0e+6GvtsJkNDEPjtrv9wPBpFlrz3QkDm2H6m92oe4H6lkhWvRMgBiz7Sz6oOaAiGY9dWIVBUABRLuBRYIMWTZNyapa+hreN4koBIEyFy3VlYKlsQQgoPuoEZlI35GGiPwbmdonwNwxfkmqVOGBKyyqFZmX0dA1Gis+YkVt1G7BbKxH0cSOw+GcmHAREgMuQpqHOrFYe6Sh6j/bIdf4ILsliGYdRJOe9mCJQKryAgRo+7fYEZB9U1bTnA9BAAiBfUBb+HfXBLvnUmEDIWRJ3pRmU588+RYuOu9CAFrnT/9eJ+tIm/lwH5TP/o31X1GvYeqcDMXph76NFcQrwbfXCX1SsCzW5Q9W5+hAPDJrmKcuP+kSTVDcEhSfFGVLLtcFQlETQYBoEGFoa4dc7WMOrqp5m0pzxEdDTdYi+6TUVxkT6xo6u4HZ7av4dtfA+2e1Zlv42KUqL1zrDsVseMiFB4dzasJFSAy4CGk+auhcjVSEW4CDAFK1F4IogPgVKAEZXWcMRa3PFfNcpa/9CqXKC8UvQ7ToYcxJgOLyszwQ0UR9PrLGN74/UI/cLvj2/96HpWsq/AfqQHw0mqF4afM6Zp6lAKKNiibFIwMg0CeZIFqprwiRFUAQWHUKkQiIJ0Arc9wBenwijdCQgEKXMsKWosIRjGEOqQgtwdiKMmmPm+DzUpUX1h5tqOU8GhYfhBCN82hjjgGanvcRKVgaTCQN2yeyb4yKoa0dyVc03HeIw+Gc3HAREgMuQpqHGj73H6yDoBfpEoNPpl4cYdUa6jJG7tRzY56nf/5ZWDj6nzSHBCEXVVNBEjwlFZCOeOMeG49DszcAAHRJZuiSTHD/eijKj6N22V7mbyaqJleE5iDIQW8OqcpL81B0AgSDSK3g5bD/QqJAXVtdEqAo1KcjCFtCaZ8I69mZcK+jOStEUuDf69SMxbezGoZsOwIH66I8QxoSBYFyN9y/aa3Wj4X4iDzG3CFRszwU5VwabEgXK28I4MstHM7pCBchMeAipHkcnP4TiEz7kogmPRSf1hY7fNKvt/w2aNsOQYClSyr0wcTDppbUhnepNRUkaZrEqRjbOuA/UEu71AYTZ8UEI2xFmbB0TUX1VzsQOOyGoBdpr5mgBwdkQn9E0LwPQQBkBYKJ5q3okkzBclo/dIkmZNzbK2ZkQtOrJskEudpH++aIAty/HNLkfjQ1GRQ4duJDcQdQuzrU00U9hgQUOJdr+7BYe6TBvbEi6hzhHXMbe10Oh3NqwUVIDLgIaR7lc34DIYRFDfTJZlZGqXZ5/eGPtbj04etjHr9v0vc0EiETiHYjDBk2PPDm37Dgxy8bPYZw4aGiNq9TPBLtUmvSAQGFmYMptX5AAQS7HinDzoC/1BVaUlLFiSo2FAIowccKWAM8hKWiqOZl8WzCgej+JwBgbJ8IKAT+PU7NdtWLJB6R1zGfkUQN4xqgOeIj8ji1L0vtiv1QwpaUIgWGiuO8tqj9XmsmxsUHh3P6wkVIDLgIaR41xbuhmY0BzWRcXyRj3+RV1OtDB5RU7MDQN25v9HUltx+iUYfqL3cgcMitec5UkAS5ygv3H4epaAhGWUSLHiBgjeysvdIhlbuh+GRqOy8pgBx2IiHsB2D26opXhmjWRUUq1KWp8InY2iMNugQjKt4tiRqj4pMQOFCnsay3dE+DY2DbuPcdlWzayFbzni1H4N8XKgtu7HGRyzyRQsu3sxqCQRflTBqvBw0XHxwOh5uVcVoQOpGx0DwhDQqQNeMWIDchC4pfQv6MwY2+0rInP8ZZ553NrlU+5ze21ENkAtGogzE/Aa61ZbRaJYhoMUCXZIJo0lOx4aJuq+5fD9ElFb/CclHYLYmgeS16EYYsGxU2tX5miS6adHCcn8PuVY3EGLJsmtcjvORU8UiwdEuD7PSzqIGgF+HbVQNTQVJcYdDcZFOACq7wKIS1VxsY2lgbdWy4gHCcn4PalftRuXAr7foLatWvCi4haNkf69imjJfD4Zz68EhIDHgk5OgJn3jiCZB9k75H7jPnNfqcNw+8GjNHPaVJYAyvxgFCyZ/+g3UQTTootdSnRHAYYOuTCcXpR6DcTQ3CZLBEVACADproh5BghCCG+tu0uetMSJUeuDeEogHWM9Pg/j2U7xCegxJLfKjltYFDLiiuALsX364a1iU31iTtL3XB84c2r6Ipk3n430PQC0i4IK+evUOER00UdwCBMm0lE3NnjdFfhosPDofTEFyExICLkKNDnXzSL+8Ef8DfwN4Nc2D6j5rqENGkg/3ctnB+txeudWW0vNakA5EJ60ej5nnAKMKQZYdgECCVe0I5HipqpEMnAAECGESAEIg2A/PisJ+TBZ3DGJpUCYESUCAGS2VjkTgkH9X/3Ql/0IJdFR++nTUACLsXY5YN/lKX5rhwmptsGu/4ph5LCIH7l0PQJZkRbsFSX6IsFx8cDqexcBESAy5Cmkd4uL+plSyR7Ju4EtAL0CWYkDaqK4s2qImNikeizeLUiVGtqFEI/QkiOoxUkBBQUcKeAO1eKwoQjDooXgmCQQcSkOE4NwcAYGqXAPMZyVHLLOF5HqrTp/u3wwiUu1kzNXVfqcoL8xnJkCo8mmMt3VJhzLbHdReNnMgthSkw5jS+C+zRCIHKj7ZArvFFRZdM+QlIvKT9Mbkmh8M5PeE5IZwWo/b7AyAKQXI9E1V97Ju8iv5CaOKotWcbCAYdEyDGLBsOv70JgbK6UL8YCXQZRSK0fFYU6O/B87CIiJpUGmwcp3hDNvKKRwJRCPQpZmZhHmspRRUQqt+FCpEV+PfXsqgHELKi1yebIVV42LFqVEWu8bFJO7zNfHOTTVWOtuLFt6MaUnVIfBjbJzYoKLn44HA4zYWLEE6L8f1vP+DKR29s0jEHpv8IICgWQJdaIAoaW3KiELh/PYQ6vwLilUIRDQWAXqBREEmh4kM1DlNLanXBfUD/FQ10CUVtIEeCFTKGNAtbYqgp3hPVt8TSNQ2O86IrVfz7alG9eCft76IXNeIDACtRDs+ZiIx+EIUc9UR+tC6n7t8PM7t4demrpZrUcTgcTjy4COG0CE3p2bL+r18i3ZRM/TUIoNQFqLOoAuhTQ7kfvp3VtI+LAm0eB0DFhSiGlmMUAISwaIcuyQzBKEIw6CCVuwGTCL3DBMEgwtDWwZZL5GoqGhIvbQ/v1ipUf72LXjNIPI8O17oySFW+UFIsAfQpZog2autuapcAiGJUY7bwidvSJeWoJ/LAIZcmMdZxfluIptj/rV1ryyAFPVxUfDurobgC0NkNAAxcfHA4nOMKFyGco2Jzt+7wBQIN7vfkJffj7p4jAJPIBIXiCkC06mHIsUNxS9DZDfCXuWj/FrVUVq1eCS6niHaj1rnUH0r0EBON0CUaYT4jhYqDI14oXi/r1yIYRAQOe9j+agM5U0ESvFurNDkfas5GJOETsGt9GaAQaoYW9BsxFyRBMOpiTszhuSWmgiR4thxhzzV1Io+MZJjyE2DuFN0NN55hWrhZmmgzwJiXgKRL619G4+KDw+G0NFyEcJrN5m7dAVmGSYzfjbWkcxcAgOOsEbTyBKDJmzqBdpkNEASCuRRypYcKDjXqIQAw6WipbQ1NLlVcfrrMEswJERON0DmMMOY4EChzwVSQRMVBULgYs+3MACxQ7tZYx4smPevPYsi219u7JHwCVjwSvNuogFB8MvSpFpjaJUC0GeutGIlMbLX2SAs192sC9YmBWLbpKvYB2ahbQ63WVQHCIx8cDqc14SKE03zkkKnGpk6d0W3bVgAh4aHBEBG5kAnVGjIJeXMIoAJDL9DtEgG8MpSATJdfFAB6EcYsGxCx/OPb64Ro1MG1vgz6JDOkaloSK7sC8O2qob4hFvp2V/M1jO0TIQgCxGDEI3LpBIiegGWnD94/q6B4JIhGHSyFqdCnWuJOzN4/q+BcSiMWxlwHBIMu5nUaQzwx4Fy+j3bpjcDcIQmmgkR2XN2agxohJFr1cR1Zj8YUjcPhcBoLL9GNAS/RbZjNXQqbfIxj+Bv0FwFBUUK0HWjliAMEAMHuu8ZsO4ztE+EPmnqp1uZqGam5YzKkSg+IQmjZrUkP4pMQKHeDSAoMWXbogvkahkxbg83TIid81VY9UOEG8SvQ2Y2w9kqPOzETheDwm7+zx42JOMQjlviIt8wSr8yXEAK5wgN90CG1vnGHL/PUty+Hw+EcLTwSwjm+mKioEM36aOMwgCWa6pJNsJ6Vwb65E5mw6IFcF4Bc6weRFOiSzDB3SILiCsCY64BnyxEQvwx9splGP4w6GLLtSL+nJzPfChcgDYkPS/dUVH+xg4kdQSfCkG2Nm7Dq210D75/VmiZ6DTWgi4dGRASrb2KNsWGDM/ra6dtYYWqfCHPHpKhrEUmBc5l2GYeLDw6Hc6yJv5h/nJg1axbat28Ps9mMoqIifP/993H3HT16NARBiPrp1q2bZr9PP/0UXbt2hclkQteuXfH5558f69vgNAajSJdU/ArL8WDoBMAkwtguAY4L85gA0SWZqADRCfBurwIABA7WQRdsIJd2UxcQSYH/QC3cvx1mAiRwyA1jth2WM9sg/Z6eqP3+AK22CfZmMWRYo6IG4ZN3wkV58O6oQsX8TZCqvNDZ6fVsRZkxRYV6fLgAMRUkNUuAeP6oYDkk9FyECRCA5pIkDslnPwBdjoq8h1BJcainT6QAUXwyaor3aARI+Hk5HA7nWNKqkZAFCxZg/PjxmDVrFgYOHIg5c+bg0ksvRUlJCfLyontb/OMf/8Dzzz/PHkuShJ49e+L660Ot4X/44QeMHDkS06ZNw9VXX43PP/8cI0aMwKpVq9CvX7/jcl+cOPgj8hZ0oKWtmTaIJh3L0QjHt6sGgiCAEEIrWdolwrebCgnfzmpUfriFNqITBUAArN3T4D9QB0MGXXZIvrIDPJsq4CmhZayRyyKxogqHXt9Ak1uDhHuWOM7X5lBoohUyAfFJMBUkUcHSJ6NJL4/iDmg67Bqy7CyPpbEW6eq+NcV7mHut7ax06NMsUdeqXX0w6jgOh8M5nrRqTki/fv3Qu3dvvP7662xbYWEhhg8fjunTpzd4/KJFi3DNNddg165dyM+nH6AjR46E0+nE119/zfa75JJLkJycjA8//LBR4+I5IQ1zVDkhoA3lQABDGzo5hi+PlM/5DYpbglTthWjRQ2c3wtw5BTqbAe6NoeZxUpUXkAl0KWYIosCECT1fIhKHtNNUpbS5ozuEoFlZLPFR8eEW+PfUsG22okxN/oVgEJEwODfm8aE64qa5nMpOP+p+KtUs3wg6Ecb8hHpFQeT1bUUZ0KeYETjs1jTYizyH7PSh7qcyzTYuPjgcTmvRapEQv9+P9evX4/HHH9dsv/jii7FmzZpGnWPu3Lm46KKLmAABaCRkwoQJmv2GDh2KV1555ajHzAlRuGVzk4SI47o3g8sv1F7dEPxmbmyXCMfAbOjstEHc4X9vpD4hoJEAc4ckakIGMAEiVXkhmvQQrQaIJh0TMIqb+pWoj8MFSPo9PeM6kx75ZBsOPv8T22btnoakKzqwc7B7OK9tPUmioSWPhgg/R7j4MGTZkXxVh7jHNZS3oRlrhGmZVOmB65fyuMdyOBxOa9BqIqSiogKyLCMjQxuyzsjIQFlZWZyjQpSWluLrr7/GBx98oNleVlbW5HP6fD74fCEnSafTGXdfThg6naZMt14IoT1hHEboU2iJbPo9PZmvhVzrR6C0DoFyN0SLHoJepAIEAASBOZPqk6gluuKVYSlM1TSrU31CVNQEVPs5WbEjH++VaMSHPs2K9DE92GP1GOmIF/oUM5xLtXkT4fuEb4tF5PUjPUPqO7Z2FW3YFzl+Fe/WI/DtrY35XKSjakPX4nA4nONJq1fHROYAEEIa5aEwb948JCUlYfjw4Ud9zunTp2PKlCmNGzCHUbjpD2ZYVh+Oa+kyjCpA0kZ3g+ePSk2kggQUSE4qBFUXUxV1H53dCAiALskEU4pFU+VCZG2+iW9nNfQZNkiVHtT9WMq2q8s9Zf+ohOIJRk7yE5F6o9bbRHYFYnbNjRd5iJzYpQoPXL9qIw/quEwFSY0SH5HCRTTro/rXaJJpw5aBfHud8G6tYs8JegEJF0TnWXE4HE5r0moiJC0tDTqdLipCUV5eHhXJiIQQgrfeegujRo2C0WjUPJeZmdnkc06cOBEPP/wwe+x0OpGbm9vYWzmtKdz0B4DYOSKJo+fRb/CSAkOOg3WorV15gE3wgk5EoMINBCtg7Ofm0GODyxy0yRyBUheAtWc6RIseikfSCBDFKzHXUwAIHHYDAKRDrqhck/I51SFvkU4pSLw4n4qbMCLdTW2906FPDSV2hi9thLuexvPusPfPQt0Ppex86njiEdVJ94JcTXUMANSu2A/FHxJ/6vm8f1bBtzsUydMlGGHvlxX3WpyWQZZlBBrRvoDDOVUwGo0Q63HLbiytJkKMRiOKiopQXFyMq6++mm0vLi7GsGHD6j12xYoV2L59O+68886o5/r374/i4mJNXsi3336LAQMGxD2fyWSCyWRqxl1wVAq3bGadZ1VbdP9eJ83/yHbAmJsAIhOW+KmairEIhk5A5sN9IBp1cG88zISA4g5AMOth7UkrPKQKj0aAaBI6Be1jW59M2IoyosSHpXsbiKbo/i7hvV2A2P4ekdGPmuI9wMaKqP3Uc/tLXUyAAIBjUA5Eoy5qf+mIF671h2Keo6ExALSs11/qYtsN6VZYe7aJeTyn5SCEoKysDNXV1a09FA7nuCKKItq3bx8VCGgqrboc8/DDD2PUqFHo06cP+vfvjzfeeAN79+7F2LFjAdAIxYEDB/DOO+9ojps7dy769euH7t27R53zoYcewvnnn48ZM2Zg2LBh+M9//oP//e9/WLVq1XG5p9MZtTrFmOuAd1sVoBehb2OhjeMO1DJxAgCmdonw73XS3ivJZiRdXgDFFUDtiv0Agt1d/QpEK+3sqkswwvVzKJqguAMIlNFJV6qiFu2qeNCnWZBybSeUz/kNrnVlUDwSFK8Ea68MCDpB22slItlTFTi2s9Kj7q+meA9kpx9ShRumgqT6e7jIhNm10zEnhnJcIs4ZSWPLcROH5Ed1xjXmOWDpnBLzeE7LowqQ9PR0WK3WZtnxczgnG4qi4ODBgygtLUVeXvPaUKi0qggZOXIkKisrMXXqVJSWlqJ79+5YvHgxq3YpLS3F3r1aC+mamhp8+umn+Mc//hHznAMGDMBHH32ESZMm4cknn0SHDh2wYMEC7hFyHEi4IBeHd1ZTAQLa2p64JEh1AeiTzTBk2GDMccC3s5otL1i60AnTsznUUdZ/gFbHiEaR9jgx6uDeQJc/wvMzVFFjK8qEXO2Foa0DokkH385qTVTG2jsDgiDAMTAbopVat3u2HIF/XyiZU0U9f7ivRvjyTPg+jvNzIJqioxqNafgWuY+5czJMefHLwSOjH7Xf79dsM5+RBFO7xLjHc1oeWZaZAElNTW3t4XA4x5U2bdrg4MGDkCQJBoOh2efhvWNiwH1Cmkf5nN9YeW14szhT+0RAEDSeG2rEIbKHi/ocgJhLLuoxqgAxFSTBcX4Oalfup83rgpEWNTqiEquaJfy5mMssAAAC386Qd0h9DqgNiY/mNIWLl2eiYumWCmMwF4ZzfPF6vdi1axfatWsHi8XS8AEczimEx+PB7t27meN5c2n16hjOqYP/YB0Egwh9shmCXtS4k4Z7dKiiIrKHS2RCqFTpgVzjA1EI9AkmyHX+0JJLspkJArXMVp9shuKWYOmWGpUAGmXudXYm9Ek0D8i9sQLSES/kaq9mmUUqd0PxSEzoxIp6xDp3pLDwlFSy6E68fRpz3nCsvdrAEGxGx2ld+BIM53Skpd73XIRwWgz1G3mbu8/UvEHDJ9NAWPJkuEjx7gj1XLH3z0bdD9RSXI14yHV+6FLMkI9QoWA7myacqsmmuiQzjPkJEHR0mUc166pPINQU7wEIYR15VeGScEEunMv2QZ9ef8fZpjeSa7r48O91whi2TGPrmwl9Ik+iPtWQ61xwrVkNuaYGusRE2AYMhM5ua+1hcTjHHC5COC1GQ9UkJCAzb47wfX17nXD+j+7X5o4eOPzWRiiuAKQaHxM2LFcjyQz374fZkgwAmDsmQZcYCgc6BuWwBFeVxCH5ICTaMVUVIOHjaciAzL2hHIHDHvY44aK8uKILgCYXpT6IQuD8ji7XqFEiVYDYB2RDZ2v+uivnxERxu1H+yiuoXvgxiNfLtgtmM5JGXI/08eMhWo9/xGv58uW44IILUFVVhaSkpON+/ZbmVLufUwkuQjjHjMjJ2L+vNkYDud0s5yJlRGccfitk227MtsPYPhFJF9MeMJ6SCigeCfpkM42QtLECksIEiCHThkCZSyNADOkWBMo9UWMxpFkQqPDAVJCEhL+ETLzqEyCyK4C6NaGmb+FLOopXYg3j4h1fH+FLVbpEU1jyq9Z+nXPqoLjd2HPrbfCWlACK1myPeL2oeu99eH75FfnvzG8VIcLhHA/4pxunxYmXyxCrg60qQIztE1H2ynoANKlVzfkgCkHlR1vg20330yeboUsILkdICkwFSSCyQk3PgiW7vt01rFIkUB4WsQhzFFXHaMyxQxAFKD4ZtSupeDFm22Dplhb3nnR2A+z9s+Pea1PEh+KTNOZtbElocC4Ew9EbAXFOXMpfeSWmAGEoCrwlJSh/5RVk/u1vx3dwrYDf7z9qzwnOyQf/lOO0KFFLEWE242oHWnU/385qEIWAEIK61TSKIFr0yH68H9JGd0f14p04/ObvTIAknE+Pl50+aAj2liFBB9HwUtXEIfnsJ1KAAIClMJW2vQ8KkISL8jQCpKZ4T1R0xN4/O2q7IdPKrtNYaor3oGLeJvh2VsOQaaNRmQvz6Fi5ADmlketcqF74cXwBoqIoqF74MRSXq/79mojP58ODDz6I9PR0mM1mnHvuuVi7dm3UfqtXr0bPnj1hNpvRr18/bNy4kT23Z88eXHnllUhOTobNZkO3bt2wePFi9nxJSQkuu+wy2O12ZGRkYNSoUaioCBn7DR48GPfffz8efvhhpKWlYciQIbjxxhtxww03aMYQCASQlpaGt99+GwCtMnvhhRdQUFAAi8WCnj174pNPPtEcs3jxYnTq1AkWiwUXXHABdu/e3eBrIggC5syZgyuuuAJWqxWFhYX44YcfsH37dgwePBg2mw39+/fHjh07NMd9+eWXKCoqgtlsRkFBAaZMmQJJCvV6mjlzJnr06AGbzYbc3FyMGzcOdXWhRHW1BcmSJUtQWFgIu92OSy65BKWlpTgd4J90nBZDM7l3SQn6WVBxYWqXwCbWmuI98G47QitSqnwsWdXUPgnpY3uiZsluVMz7A/59IYOzpEvaw7ONeolIVV4IBlqp4ttZDUEUYCpIgmDUwZTn0AiP+sYYqzRXze2IJT7U/SP7tSQOyYe1R+PdSQMVHpTP+U0T/Ui6sgO9vo5XWpwOuNas1uSA1AfxelG3enWLXv+xxx7Dp59+ivnz5+OXX35Bx44dMXToUBw5ckSz36OPPoqXXnoJa9euRXp6Oq666ipmT3/ffffB5/Nh5cqV2LhxI2bMmAG7neZwlZaWYtCgQejVqxfWrVuHb775BocOHcKIESM0558/fz70ej1Wr16NOXPm4Oabb8YXX3yhmaSXLFkCl8uFa6+9FgAwadIkvP3223j99dexadMmTJgwAbfccgtWrFgBANi3bx+uueYaXHbZZdiwYQPGjBkT1a09HtOmTcOtt96KDRs2oEuXLrjppptwzz33YOLEiVi3bh0A4P7779eM7ZZbbsGDDz6IkpISzJkzB/PmzcOzzz7L9hFFEa+++ir++OMPzJ8/H0uXLsVjjz2mua7b7cZLL72Ed999FytXrsTevXvxyCOPNGrMJzvcJyQG3CekedQU79E0SouVX1G5cCt1Q3UFIBh1IJICY5YN+jQrdIlGjScHEHRH9UgACFzrD0E061kX3sb0YQknvKNsLAESOWZ1u39/rcZMrSnXjEQ1UQMAY14CEi9px0s8T1JUn5Dm+CRUffwxyp6c3Oj9M6dNRfL11zd1iDFxuVxITk7GvHnzcNNNNwGg0YZ27dph/PjxePTRR1ki50cffYSRI0cCAI4cOYKcnBzMmzcPI0aMwJlnnolrr70WTz31VNQ1Jk+ejJ9++glLlixh2/bv34/c3Fxs3boVnTp1wuDBg1FTU4Nff/2V7RMIBJCdnY2ZM2di1KhRAICbbroJkiRh4cKFcLlcSEtLw9KlS9G/f3923JgxY+B2u/HBBx/gb3/7GxYtWoRNmzax/1uPP/44ZsyYUW9iqiAImDRpEqZNmwYA+PHHH9G/f3/MnTsXd9xxBwDgo48+wu233w6Phy7znn/++bj00ksxceJEdp733nsPjz32GA4ePBh9EQAff/wx7r33XhYVmjdvHm6//XZs374dHTp0AADMmjULU6dObVRH+dbiaN7/4fCcEE6LUV+H2dqV++HZXAmpygvFLUHQiRAMIow5DhC/DKnSA6nSA0EvsooQ7/Yq1P1wEIJRhOKRWK5IZG5JY6lPgMQSH5FRj8h7bAqVH22BXBNaRqrP9Ixz6qNLbJq7bVP3r48dO3YgEAhg4MCBbJvBYEDfvn2xefNmzb7hE31KSgo6d+7M9nnwwQdx77334ttvv8VFF12Ea6+9FmeeeSYAYP369Vi2bBmLjERev1OnTgCAPn36aJ4zGAy4/vrr8f7772PUqFFwuVz4z3/+gw8++AAAXeLxer0YMmSI5ji/34+zzjoLALB582acc845GnEffh/1oY4fAGt62qNHD802r9cLp9OJhIQErF+/HmvXrtVEPmRZhtfrhdvthtVqxbJly/Dcc8+hpKQETqcTkiTB6/XC5XLBZqNl2FarlQkQAMjKykJ5eXQX7lMRLkI4LU7kxH143h8gPpmamelFiFbaCdeQbEbgkIslm6pW6e7fyiHX+gGEnFcN6VZk3HfWUY/JemYa+93WOx2KR9IurwzOhXP5Ps0261npMKQ1zxEz0vK9zV1nstwUzumLbcBACGZzo5ZkBLMZ9jDBcLSowe/ICBwhpFFROXWfMWPGYOjQofjvf/+Lb7/9FtOnT8fLL7+MBx54AIqi4Morr8SMGTOijs/KCnV1VifhcG6++WYMGjQI5eXlKC4uhtlsxqWXXgqA9iwBgP/+979o27at5ji1CenRBPfD7cfV+4y1TR2HoiiYMmUKrrnmmqhzmc1m7NmzB5dddhnGjh2LadOmISUlBatWrcKdd96p6bocaXsuCMJR3cfJBBchnBbFs1W7bKFOwP4DdUx8hFurmzunQCp3MwHi+rmUtai3D2gLyAoEgw6OQTnNHpMqKEhAYdGQhAtz4VwaalxnKkiAb6cTzuWhbc2NeqjX9O9xsi7BzY3ecE5NdHYbkkZcj6r33q8/OVUUkTTieogxJuvm0rFjRxiNRqxatUqzHLNu3TqMHz9es++PP/6IvDy6vFpVVYVt27ahS5cu7Pnc3FyMHTsWY8eOxcSJE/Hmm2/igQceQO/evfHpp5+iXbt20OubNs0MGDAAubm5WLBgAb7++mtcf/31rGqma9euMJlM2Lt3LwYNGhTz+K5du2LRokVR93Es6N27N7Zu3YqOHTvGfH7dunWQJAkvv/wya3u/cOHCYzKWkxUuQjgthuKX4d8bagqnVr8EylyAALakIjl9EADoUy3Q2Y3Q2Y1wrQ+ufeoEViFTU7wHEHUwZtshGmNbpjcE89/YVUN72ARRBYh/f22wqZ6TPXe04gPQ9r/h4oMTi/Tx4+H55df4ZbqiCHPXrkiPEAZHi81mw7333otHH30UKSkpyMvLwwsvvAC3240777xTs+/UqVORmpqKjIwMPPHEE0hLS8Pw4cMBAOPHj8ell16KTp06oaqqCkuXLkVhYSEAmrT65ptv4sYbb8Sjjz6KtLQ0bN++HR999BHefPNN6HTx/z8LgoCbbroJs2fPxrZt27Bs2TL2nMPhwCOPPIIJEyZAURSce+65cDqdWLNmDex2O2677TaMHTsWL7/8Mh5++GHcc889WL9+PebNm9eir6HK5MmTccUVVyA3NxfXX389RFHE77//jo0bN+KZZ55Bhw4dIEkS/vnPf+LKK6/E6tWrMXv27GMylpMVXh3DaTHCTcIUPy1RU707GAQQRAG2s7NgzEuAd3sVfDurWXTEVpQZEiBBLN2a16FU0yyvfaJmWUT93ZjjAAAIBrHJJbaR11KXXlS3Uy5AOPUhWq3If2c+km+5GUJEYp9gNiP5lpuPmVHZ888/j2uvvRajRo1C7969sX37dixZsgTJyclR+z300EMoKipCaWkpvvjiCxaVkGUZ9913HwoLC3HJJZegc+fOmDVrFgAgOzsbq1evhizLGDp0KLp3746HHnoIiYmJLCJQHzfffDNKSkrQtm1bTe4KQCtYJk+ejOnTp6OwsBBDhw7Fl19+ifbt2wMA8vLy8Omnn+LLL79Ez549MXv2bDz33HMt8bJFMXToUHz11VcoLi7G2WefjXPOOQczZ85kneB79eqFmTNnYsaMGejevTvef/99TJ8+/ZiM5WSFV8fEgFfHNA8iKRD0Isrn/AbFFYBc6wdR6NtLNOsBgZqN2XpnQKr2abvjBjvt2nqnw/VLKCGruZO48397QIi2A26srr0Jg3NYuW9zCBdLkQ35OKc2LVUdAACKy4W61aHeMfaBA1t0CYbDaWl4dQznhKPuh4PwlNAKGMgERCEssdRWlMkmadcvhwAAokkPQ1tt9nxLCBDFI8F/sA7+g3XQJ5uZnTvQ9LLeeMQSH1yAcJqLaLMh4eKLW3sYHM5xh4sQTovBBAgBdEkm6PUiiz74dlYDInU2NeYlQNCLUaWxlsIU5sdxNBP5odd+BZFCa+yi1XBMxIcKFx8cDofTPLgI4bQYxvaJmiUPJj6CqHbqatdZtQsuQJ1H1Q6yzZ3M5Vo/Dr32K0uAtXZvA8Gkg7ljkiYptTnE64cD0HyScEt6DofD4TQOLkI4LYZjYFvUrTnIBIhKeA5GuMBwrTvEtqmTfHMFSPW3uzX9Z2xFmS0SmYgUH+FiCeDRDw6HwzkauAjhtBhqm/vIjrBA9GQdLjrU3xMuymvyNSs/3AKpyovAIZrzoU82I3N8UZPPE0k8B1VVgBjzHLB0Tjnq63A4HM7pDBchnBYlUObSVp8El17CCXcsDXcybUoPFbUHi1TlZcsvLRH9iCU+FJ/WVZVHPzgcDqdl4CKE06IYMkNlhQ11sQ2vhDFkNK4cMbwBnFTlhSHbDuKRjtqTI16PGI19e682MLRpec8GDofDOV3hIoTT4sQTA/GSOxsSD4pXQsX8TZptpoIkGAmBf1fNUQmQeOJDqvS0SLkwh8PhcOLDRQinxahvopaqfTG313dMTfEeyDU+SJUetq3NnT3gXBa0XD8KAVJfd9zw5xzntaVGaxwOh8NpcfinK+e44FpLe8MY0iwIVFBRUW/ERCHw7aZup6LVwEpgVQFCfHQJJuEvjU9mJYTA+b+9mm3hY/D+WQXf7pbpIcPhcFqHwYMHo1evXnjllVeO+7UFQcDnn3/O+utwGoaLEM4xR40sOM5ti9pVtIy2vnwR1telfSIEQYgyNQMAwaSHMdsOQWw4mZUoRFNWG+v64edP+Eteo87L4ZysxJuoFy1ahKuvvvqEaCPfrl07jB8/Pqqzb0N89tlnMBgMjd5/9+7daN++PX799Vf06tWraYOMoLS0NKr/Dqd+uAjhHFNY9ctZ6TEFiP9gHTybKgFEl/bGSg4Np6HGdkRWWLdclUjxUbvqABSPFPd5DodzfPH7/axJXnNISWm90vnMzMxWu/bJSqt30Z01axZrgFNUVITvv/++3v19Ph+eeOIJ5Ofnw2QyoUOHDnjrrbc0+7zyyivo3LkzLBYLcnNzMWHCBHi93jhn5BwrwsWD+1ea5BkuLGqK98CzqTJm59mGBEh9YoEEZOrpESZAYnXIrSnewwTI0XTQ5XBOVZ5++mn06tUL7777Ltq1a4fExETccMMNqK2tZfsoioIZM2agY8eOMJlMyMvLw7PPPsueP3DgAEaOHInk5GSkpqZi2LBh2L17N3t+9OjRGD58OKZPn47s7Gx06tQJgwcPxp49ezBhwgQIgsDK9ysrK3HjjTciJycHVqsVPXr0wIcffqgZ8+DBgzXRk3bt2uG5557DHXfcAYfDgby8PLzxxhvsebX77llnnQVBEDB48GCsXLkSBoMBZWVlmnP/3//9H84///y4r5cgCFi0aBEAGmERBAGfffYZLrjgAlitVvTs2RM//PBDva+5IAiYM2cOrrjiClitVhQWFuKHH37A9u3bMXjwYNhsNvTv3x87duzQHPfll1+iqKgIZrMZBQUFmDJlCiQp9AVr5syZ6NGjB2w2G3JzczFu3DjU1dWx5+fNm4ekpCQsWbIEhYWFsNvtuOSSS1BaWlrveI+WVhUhCxYswPjx4/HEE0/g119/xXnnnYdLL70Ue/fujXvMiBEj8N1332Hu3LnYunUrPvzwQ3Tp0oU9//777+Pxxx/HU089hc2bN2Pu3LlYsGABJk6ceDxuiRMklnhwnNeWiQ+ARj5kVyCm+CAyYfuJZh2svdqw88QTC4qX+nk4l+/X7BtLfHDfDw6ncezYsQOLFi3CV199ha+++gorVqzA888/z56fOHEiZsyYgSeffBIlJSX44IMPkJGRAQBwu9244IILYLfbsXLlSqxatYpNbn6/n53ju+++w+bNm1FcXIyvvvoKn332GXJycjB16lSUlpayidDr9aKoqAhfffUV/vjjD9x9990YNWoUfvrpp3rv4eWXX0afPn3w66+/Yty4cbj33nuxZcsWAMDPP/8MAPjf//6H0tJSfPbZZzj//PNRUFCAd999l51DkiS89957uP3225v0+j3xxBN45JFHsGHDBnTq1Ak33nijRhzEYtq0abj11luxYcMGdOnSBTfddBPuueceTJw4EevWrQMA3H///Wz/JUuW4JZbbsGDDz6IkpISzJkzB/PmzdOIQVEU8eqrr+KPP/7A/PnzsXTpUjz22GOa67rdbrz00kt49913sXLlSuzduxePPPJIk+63yZBWpG/fvmTs2LGabV26dCGPP/54zP2//vprkpiYSCorK+Oe87777iMXXnihZtvDDz9Mzj333EaPq6amhgAgNTU1jT6GE0Kq9pLqb3ezn6pvdpHD72xij8vf2qh5PhLnqv3sOUVSCCEk7r6EECLV+jTni7df+Hnq24fDaQwej4eUlJQQj8cT9Zy7pIK4fj103H7cJRVNGvugQYPIQw89FLX9888/J+HTwlNPPUWsVitxOp1s26OPPkr69etHCCHE6XQSk8lE3nzzzZjXmTt3LuncuTNRFIVt8/l8xGKxkCVLlhBCCLnttttIRkYG8fl8mmPz8/PJ3//+9wbv5bLLLiP/93//F/fe8vPzyS233MIeK4pC0tPTyeuvv04IIWTXrl0EAPn11181550xYwYpLCxkjxctWkTsdjupq6uLOxYA5PPPP9ec99///jd7ftOmTQQA2bx5c73nmDRpEnv8ww8/EABk7ty5bNuHH35IzGYze3zeeeeR5557TnOed999l2RlZcW9zsKFC0lqaip7/PbbbxMAZPv27Wzba6+9RjIyMmIeX9/7vym0Wk6I3+/H+vXr8fjjj2u2X3zxxVizZk3MY7744gv06dMHL7zwAt59913YbDZcddVVmDZtGiwWCwDg3HPPxXvvvYeff/4Zffv2xc6dO7F48WLcdtttccfi8/ng84VKSJ1OZ9x9OQ1T9zMNYfoP1IH4qOI3FSRB8UkQTXoYcxwAAHv/LOjs2rXfWBGKeH1lpGofq7qJPCaS+kpyOZyWxlJYf77SyUS7du3gcDjY46ysLJSX0+XVzZs3w+fz4S9/+UvMY9evX4/t27drjgdoRCN8OaFHjx6NygORZRnPP/88FixYgAMHDrDPbputfrPDM888k/0uCAIyMzPZPcRj9OjRmDRpEn788Uecc845eOuttzBixIgGr1XftbOysgAA5eXlmgh+fceoUaUePXpotnm9XjidTiQkJGD9+vVYu3atJvIhyzK8Xi/cbjesViuWLVuG5557DiUlJXA6nZAkCV6vFy6Xi92T1WpFhw4dNONt6HU6WlpNhFRUVECWZfYCq2RkZEStw6ns3LkTq1atgtlsxueff46KigqMGzcOR44cYXkhN9xwAw4fPoxzzz0XhBBIkoR77703SuyEM336dEyZMqXlbu40JrLCBQBMHZIAAogm+nbTp1lgOys97rFAtABxDMxmzwUOu+HecFhzbEN+I43Zj8M5XUhISEBNTU3U9urqaiQkJGi2RVaaCIIARVEAgH35i4eiKCgqKsL7778f9VybNqEl1sZO7C+//DL+/ve/45VXXmH5DePHj9cs7cSivnuIR3p6Oq688kq8/fbbKCgowOLFi7F8+fJGjTPetdXcloauHeuY+s6jKAqmTJmCa665JupcZrMZe/bswWWXXYaxY8di2rRpSElJwapVq3DnnXciEAjEvK56HXKMK6VavTomsl8IISRuDxFFUSAIAt5//30kJtLW7DNnzsR1112H1157DRaLBcuXL8ezzz6LWbNmoV+/fti+fTseeughZGVl4cknn4x53okTJ+Lhhx9mj51OJ3JzeWv2phJVYpufAEEnAmHv4cZEKmIlpYpWA/wH6uApqWTbBAFIuKhx4kPQC0i4oOkN8jicU5EuXbrg66+/jtq+du1adO7cudHnOeOMM2CxWPDdd99hzJgxUc/37t0bCxYsQHp6epS4aQij0QhZljXbvv/+ewwbNgy33HILADon/PnnnygsLGzSuSOvAyDqWgAwZswY3HDDDcjJyUGHDh0wcODAZl/nWNK7d29s3boVHTt2jPn8unXrIEkSXn75ZYgiTQVduHDh8RxiXFpNhKSlpUGn00VFPcrLy6OiIypZWVlo27YtEyAAUFhYCEII9u/fjzPOOANPPvkkRo0axf5D9OjRAy6XC3fffTeeeOIJ9gcIx2QywWQyteDdnb4oLr+mgZ1KPPEhO/2o+4kmnZk7JcOUTz+owgWEuUOi5rHOZoB9QDbiEekLwqMfHI6WcePG4V//+hfuu+8+3H333bBYLCguLsbcuXM1yZgNYTab8de//hWPPfYYjEYjBg4ciMOHD2PTpk248847cfPNN+PFF1/EsGHDMHXqVOTk5GDv3r347LPP8OijjyInJyfuudu1a4eVK1fihhtugMlkQlpaGjp27IhPP/0Ua9asQXJyMmbOnImysrKjEiHp6emwWCz45ptvkJOTA7PZzOaYoUOHIjExEc888wymTp3a7GscayZPnowrrrgCubm5uP766yGKIn7//Xds3LgRzzzzDDp06ABJkvDPf/4TV155JVavXo3Zs2e39rABtGJ1jNFoRFFREYqLizXbi4uLMWDAgJjHDBw4EAcPHtSUFW3btg2iKLI3s9vtjhIaOp0OhJATwoDnVCbhojyINu26bn2lrzXFe5gASRySzwSIcxkVEFKFGwDg3UHDxvpUMxKH5NcrQGqK9zABYsyxcwHC4cSgXbt2+P7777Fjxw5cfPHFOPvsszFv3jzMmzcP119/fZPO9eSTT+L//u//MHnyZBQWFmLkyJEsj8BqtWLlypXIy8vDNddcg8LCQtxxxx3weDwNRkamTp2K3bt3o0OHDmzp5sknn0Tv3r0xdOhQDB48GJmZmUftTqrX6/Hqq69izpw5yM7OxrBhw9hzoihi9OjRkGUZt95661Fd51gydOhQfPXVVyguLsbZZ5+Nc845BzNnzkR+Pv3869WrF2bOnIkZM2age/fueP/99zF9+vRWHjVFIK04My9YsACjRo3C7Nmz0b9/f7zxxht48803sWnTJuTn52PixIk4cOAA3nnnHQBAXV0dCgsLcc4552DKlCmoqKjAmDFjMGjQILz55psAaF37zJkz8cYbb7DlmHvvvRdFRUVYsGBBo8bldDqRmJiImpqaJocQT2eaknsRb1/FK+HIx9uguAMsomLMtjdoTKb4ZNSu1JbmcjjHEq/Xi127djGfI86pyV133YVDhw7hiy++aO2hnFC01Pu/VXNCRo4cicrKSlYL3r17dyxevJipt9LSUo1niN1uR3FxMR544AH06dMHqampGDFiBJ555hm2z6RJkyAIAiZNmoQDBw6gTZs2uPLKKzVZw5xjg7ljEox5CRB09VuexxMgdWsOwr2RJpxS75BEmDskNXjd8PNZe7aBId3axJFzOByOlpqaGqxduxbvv/8+/vOf/7T2cE5ZWjUScqLCIyHHjlgCxPndXhCFsITWpMsLWBlvfUhHvHCtPxR1Pg7neMAjIac2gwcPxs8//4x77rkHf//731t7OCccp0QkhHP64N1RDd9OmtthH5ANnc2gESS+ndUwZNhg65cFY1bD5XrhxzrObQvRwt/KHA6n5WhOOS6n6fBPbs4xJzL6EWkcpnilUP5HAwIkXMyo5+NwOBzOyQkXIZxjSqTgCH9s75+Fuh9KIZrp27ApyawJf8mDINafe8LhcDicExsuQjjHjHgdcNXlE++2KratPgFSt+YgZFegUftyOBwO5+SBixBOi0MkBc5l+6K2OwblQDTq6D4KgW8P7dHDLdc5HA7n9ISLEE6Lola6hJNwQS4EvRi1H8AbznE4HM7pDBchnBYjUjjEy9tQ90u4MHYvFx794HA4nNMDLkI4LU7CRXlxmxCqAsOQYY0yNePRDw6Hwzm9aLXeMZxTD7VPTEMCBACsZ7aJ+1x9/WY4HM7RM3r0aAiCgLFjx0Y9N27cOAiCgNGjRx//gXFOO7gI4RwX4i2x1BTvYc8JosDFB4dznMjNzcVHH30Ej8fDtnm9Xnz44YfIy4u9VMrhtDRchHCOOVJl6ENOFRmEkChhkvAX/sHH4Rwvevfujby8PHz22Wds22effYbc3FycddZZbBshBC+88AIKCgpgsVjQs2dPfPLJJ+x5WZZx5513on379rBYLOjcuTP+8Y9/aK41evRoDB8+HC+99BKysrKQmpqK++67D4FAAJzTG54TwjnmuH6hbb1VARIuPoxt7bB0rb9DLofDOTbcfvvtePvtt3HzzTcDAN566y3ccccdGsvySZMm4bPPPsPrr7+OM844AytXrsQtt9yCNm3aYNCgQVAUBTk5OVi4cCHS0tKwZs0a3H333cjKysKIESPYeZYtW4asrCwsW7YM27dvx8iRI9GrVy/cddddx/u2OScQvIFdDHgDu5ZDFRyJQ/Kh+GXUrtjPnuNLL5yTmfoaeHk2V4L45OM2FsGkg6Ww8WJ+9OjRqK6uxr///W/k5ORgy5YtEAQBXbp0wb59+zBmzBgkJSXhtddeQ1paGpYuXYr+/fuz48eMGQO3240PPvgg5vnvu+8+HDp0iEVMRo8ejeXLl2PHjh3Q6ahX0IgRIyCKIj766KOjuHNOa8Eb2HFOeFQBYu+fFZGUoOF9awAAEvtJREFUmgZDRsNN6jick5WmCILWJC0tDZdffjnmz58PQgguv/xypKWlsedLSkrg9XoxZMgQzXF+v1+zZDN79mz8+9//xp49e+DxeOD3+9GrVy/NMd26dWMCBACysrKwcePGY3NjnJMGLkI4x4Rw0VH3Qyn7nUc/OJwTizvuuAP3338/AOC1117TPKcoCgDgv//9L9q2bat5zmQyAQAWLlyICRMm4OWXX0b//v3hcDjw4osv4qefftLsbzAYNI8FQWDn55y+cBHCaXFi9YxxDMyGaDXE2JvD4bQml1xyCfx+PwBg6NChmue6du0Kk8mEvXv3YtCgQTGP//777zFgwACMGzeObduxY8exGzDnlIKLEE6LUvv9/qhtPPrB4Zy46HQ6bN68mf0ejsPhwCOPPIIJEyZAURSce+65cDqdWLNmDex2O2677TZ07NgR77zzDpYsWYL27dvj3Xffxdq1a9G+ffvWuB3OSQYXIZwWQ/HJULyhZLyEC/OiXFE5HM6JR30J+NOmTUN6ejqmT5+OnTt3IikpCb1798bf/vY3AMDYsWOxYcMGjBw5EoIg4MYbb8S4cePw9ddfH6/hc05ieHVMDHh1TPPgPV84pxMtVR3A4ZyM8OoYzglHwuAcCAZdwztyOBwOhwPumMppQbgA4XA4HE5T4CKEw+FwOBxOq8BFCIfD4XA4nFaBixAOh8M5CnhuP+d0pKXe91yEcDgcTjNQHUDdbncrj4TDOf6oBneR3jJNpdWrY2bNmoUXX3wRpaWl6NatG1555RWcd955cff3+XyYOnUq3nvvPZSVlSEnJwdPPPEE7rjjDrZPdXU1nnjiCXz22WeoqqpC+/bt8fLLL+Oyyy47HrfE4XBOA3Q6HZKSklBeTrtEW61WCAL3xeGc+iiKgsOHD8NqtUKvPzoZ0aoiZMGCBRg/fjxmzZqFgQMHYs6cObj00ktRUlKCvLy8mMeMGDEChw4dwty5c9GxY0eUl5dDkiT2vN/vx5AhQ5Ceno5PPvkEOTk52LdvHxwOx/G6LQ6Hc5qQmZkJAEyIcDinC6IoIi8v76iFd6ualfXr1w+9e/fG66+/zrYVFhZi+PDhmD59etT+33zzDW644Qbs3LkTKSkpMc85e/ZsvPjii9iyZUtUw6TGws3KOBxOU5BlGYFAoLWHweEcN4xGI0Tx6DM6Wk2E+P1+WK1WfPzxx7j66qvZ9oceeggbNmzAihUroo4ZN24ctm3bhj59+uDdd9+FzWbDVVddhWnTpsFisQAALrvsMqSkpMBqteI///kP2rRpg5tuugl//etfG712xUUIh8PhcDjHnlZbjqmoqIAsy8jIyNBsz8jIQFlZWcxjdu7ciVWrVsFsNuPzzz9HRUUFxo0bhyNHjuCtt95i+yxduhQ333wzFi9ejD///BP33XcfJEnC5MmTY57X5/PB5/Oxx06ns4XuksPhcDgcTjxaPTE1cj2JEBJ3jUlRFAiCgPfffx+JiYkAgJkzZ+K6667Da6+9BovFAkVRkJ6ejjfeeAM6nQ5FRUU4ePAgXnzxxbgiZPr06ZgyZUrL3hiHw+FwOJx6abUS3bS0NOh0uqioR3l5eVR0RCUrKwtt27ZlAgSgOSSEEOzfv5/t06lTJ83SS2FhIcrKylhJUSQTJ05ETU0N+9m3b9/R3h6Hw+FwOJwGaLVIiNFoRFFREYqLizU5IcXFxRg2bFjMYwYOHIiPP/4YdXV1sNvtAIBt27ZBFEXk5OSwfT744AMoisKSZrZt24asrCwYjcaY5zWZTDCZTOyxmibDl2U4HA6Hw2keDoej4eoZ0op89NFHxGAwkLlz55KSkhIyfvx4YrPZyO7duwkhhDz++ONk1KhRbP/a2lqSk5NDrrvuOrJp0yayYsUKcsYZZ5AxY8awffbu3Uvsdju5//77ydatW8lXX31F0tPTyTPPPNPoce3bt48A4D/8h//wH/7Df/hPM39qamoanG9bNSdk5MiRqKysxNSpU1FaWoru3btj8eLFyM/PBwCUlpZi7969bH+73Y7i4mI88MAD6NOnD1JTUzFixAg888wzbJ/c3Fx8++23mDBhAs4880y0bdsWDz30EP761782elzZ2dnMW4SbDzUep9OJ3Nxc7Nu3j1cVcY4p/L3GOV7w91rzaYw/V6v6hHBOLXhpM+d4wd9rnOMFf68dW3jvGA6Hw+FwOK0CFyEcDofD4XBaBS5COC2GyWTCU089pak04nCOBfy9xjle8PfasYXnhHA4HA6Hw2kVeCSEw+FwOBxOq8BFCIfD4XA4nFaBixAOh8PhcDitAhchnGPO008/jV69ekVty8jIgCAIWLRoUauMi3Nic7zeG+3atcMrr7xyzK/D4XCi4SKE0yDl5eW45557kJeXB5PJhMzMTAwdOhQ//PBDs863efNmTJkyBXPmzEFpaSkuvfTSFh4x50Rk9OjREAQh6mf79u0x9+fvDU4sGvo84l9sTi5a1badc3Jw7bXXIhAIYP78+SgoKMChQ4fw3Xff4ciRI806344dOwAAw4YN47b4pxmXXHIJ3n77bc22Nm3aaB77/X4YjUZkZmYez6FxThJa4vMoEAjAYDAcw1EePSfDGFuERnd145yWVFVVEQBk+fLlcfeprq4md911F2nTpg1xOBzkggsuIBs2bGDPP/XUU6Rnz57sd0Q0OeKcHtx2221k2LBhUdsHDRpE7rvvPjJhwgSSmppKzj//fEIIIQDI559/zvbbv38/GTFiBElKSiIpKSnkqquuIrt27Yo6/4svvkgyMzNJSkoKGTduHPH7/WyfQ4cOkSuuuIKYzWbSrl078t5775H8/Hzy97///RjdNaclaejzKD8/X/PZkp+fTwgJfQbNnTuXtG/fngiCQBRFIV9//TUZOHAgSUxMJCkpKeTyyy8n27dvZ+fbtWsXAUA+/fRTMnjwYGKxWMiZZ55J1qxZo7nuG2+8QXJycojFYiHDhw8nL7/8MklMTNTs88UXX5DevXsTk8lE2rdvT55++mkSCATY8wDI66+/Tq666ipitVrJ5MmTW+ZFO8HhyzGcerHb7bDb7Vi0aBF8Pl/U84QQXH755SgrK8PixYuxfv169O7dG3/5y19ifjN55JFH2Dfh0tJSlJaWHvN74Jz4zJ8/H3q9HqtXr8acOXOinne73bjgggtgt9uxcuVKrFq1Cna7HZdccgn8fj/bb9myZdixYweWLVuG+fPnY968eZg3bx57fvTo0di9ezeWLl2KTz75BLNmzUJ5efnxuEVOC9DQ59HatWsBAG+//TZKS0vZYwDYvn07Fi5ciE8//RQbNmwAALhcLjz88MNYu3YtvvvuO4iiiKuvvhqKomjO+8QTT+CRRx7Bhg0b0KlTJ9x4442QJAkAsHr1aowdOxYPPfQQNmzYgCFDhuDZZ5/VHL9kyRLccsstePDBB1FSUoI5c+Zg3rx5Ufs99dRTGDZsGDZu3Ig77rjjqF+vk4LWVkGcE59PPvmEJCcnE7PZTAYMGEAmTpxIfvvtN0IIId999x1JSEggXq9Xc0yHDh3InDlzCCHaSAghhHz++ec8AnIacttttxGdTkdsNhv7ue6668igQYNIr169ovZHWCRk7ty5pHPnzkRRFPa8z+cjFouFLFmyhJ0/Pz+fSJLE9rn++uvJyJEjCSGEbN26lQAgP/74I3t+8+bNBACPhJxE1Pd5REh0BI0Q+hlkMBhIeXl5vecuLy8nAMjGjRsJIaFIyL///W+2z6ZNmwgAsnnzZkIIISNHjiSXX3655jw333yzJhJy3nnnkeeee06zz7vvvkuysrI04x4/fnzDL8ApBo+EcBrk2muvxcGDB/HFF19g6NChWL58OXr37o158+Zh/fr1qKurQ2pqKvuWYrfbsWvXLpb7weGoXHDBBdiwYQP7efXVVwEAffr0qfe49evXY/v27XA4HOw9lpKSAq/Xq3mfdevWDTqdjj3OyspikY7NmzdDr9drrtWlSxckJSW14B1yjjX1fR7VR35+flT+0Y4dO3DTTTehoKAACQkJaN++PQBg7969mv3OPPNM9ntWVhYAsPfV1q1b0bdvX83+kY/Xr1+PqVOnaj4j77rrLpSWlsLtdrP9Gvp/cCrCE1M5jcJsNmPIkCEYMmQIJk+ejDFjxuCpp57CuHHjkJWVheXLl0cdwz/cOZHYbDZ07Ngx5vb6UBQFRUVFeP/996OeC59YIhP5BEFgoXUS7FDBk6FPfuJ9Ho0ePTruMbHeY1deeSVyc3Px5ptvIjs7G4qioHv37polPkD7vlLfP+Hvq8j3FInohqIoCqZMmYJrrrkm5r3UN8ZTHS5COM2ia9euWLRoEXr37o2ysjLo9Xq0a9eutYfFOUXp3bs3FixYgPT0dCQkJDTrHIWFhZAkCevWrWPfVLdu3Yrq6uoWHCmnNVA/jwAqGGRZbvCYyspKbN68GXPmzMF5550HAFi1alWTr92lSxf8/PPPmm3r1q3TPO7duze2bt0aU4Cf7vDlGE69VFZW4sILL8R7772H33//Hbt27cLHH3+MF154AcOGDcNFF12E/v37Y/jw4ViyZAl2796NNWvWYNKkSVH/ETmc5nLzzTcjLS0Nw4YNw/fff49du3ZhxYoVeOihh7B///5GnaNz58645JJLcNddd+Gnn37C+vXrMWbMGFgslmM8ek5L0dDnEUDN57777juUlZWhqqoq7rmSk5ORmpqKN954A9u3b8fSpUvx8MMPN3lMDzzwABYvXoyZM2fizz//xJw5c/D1119roiOTJ0/GO++8g6effhqbNm3C5s2bsWDBAkyaNKnpL8IpBhchnHqx2+3o168f/v73v+P8889H9+7d8eSTT+Kuu+7Cv/71LwiCgMWLF+P888/HHXfcgU6dOuGGG27A7t27kZGR0drD55wiWK1WrFy5Enl5ebjmmmtQWFiIO+64Ax6Pp0mRkbfffhu5ubkYNGgQrrnmGtx9991IT08/hiPntCQNfR4BwMsvv4zi4mLk5ubirLPOinsuURTx0UcfYf369ejevTsmTJiAF198scljGjhwIGbPno2ZM2eiZ8+e+OabbzBhwgTNMsvQoUPx1Vdfobi4GGeffTbOOecczJw5E/n5+U1/EU4xBBK5eMXhcDgcDqfZ3HXXXdiyZQu+//771h7KCQ/PCeFwOBwO5yh46aWXMGTIENhsNnz99deYP38+Zs2a1drDOingkRAOh8PhcI6CESNGYPny5aitrUVBQQEeeOABjB07trWHdVLARQiHw+FwOJxWgSemcjgcDofDaRW4COFwOBwOh9MqcBHC4XA4HA6nVeAihMPhcDgcTqvARQiHwzlpmDdvXov0JBIEgdl8czic1oOLEA6Hc1wZPXo0hg8f3trD4HA4JwBchHA4HA6Hw2kVuAjhcDgnDDNnzkSPHj1gs9mQm5uLcePGoa6uLmq/RYsWoVOnTqyl+759+zTPf/nllygqKoLZbEZBQQGmTJkCSZKO121wOJxGwkUIh8M5YRBFEa+++ir++OMPzJ8/H0uXLsVjjz2m2cftduPZZ5/F/PnzsXr1ajidTtxwww3s+SVLluCWW27Bgw8+iJKSEsyZMwfz5s3Ds88+e7xvh8PhNAB3TOVwOMeV0aNHo7q6ulGJoR9//DHuvfdeVFRUAKCJqbfffjt+/PFH9OvXDwCwZcsWFBYW4qeffkLfvn1x/vnn49JLL8XEiRPZed577z089thjOHjwIACamPr555/z3BQOp5XhDew4HM4Jw7Jly/Dcc8+hpKQETqcTkiTB6/XC5XLBZrMBAPR6Pfr06cOO6dKlC5KSkrB582b07dsX69evx9q1azWRD1mW4fV64Xa7YbVaj/t9cTic2HARwuFwTgj27NmDyy67DGPHjsW0adOQkpKCVatW4c4770QgENDsKwhC1PHqNkVRMGXKFFxzzTVR+5jN5mMzeA6H0yy4COFwOCcE69atgyRJePnllyGKNF1t4cKFUftJkoR169ahb9++AICtW7eiuroaXbp0AQD07t0bW7duRceOHY/f4DkcTrPgIoTD4Rx3ampqsGHDBs22Nm3aQJIk/POf/8SVV16J1atXY/bs2VHHGgwGPPDAA3j11VdhMBhw//3345xzzmGiZPLkybjiiiuQm5uL66+/HqIo4vfff8fGjRvxzDPPHI/b43A4jYRXx3A4nOPO8uXLcdZZZ2l+3nrrLcycORMzZsxA9+7d8f7772P69OlRx1qtVvz1r3/FTTfdhP79+8NiseCjjz5izw8dOhRfffUViouLcfbZZ+Occ87BzJkzkZ+ffzxvkcPhNAJeHcPhcDgcDqdV4JEQDofD4XA4rQIXIRwOh8PhcFoFLkI4HA6Hw+G0ClyEcDgcDofDaRW4COFwOBwOh9MqcBHC4XA4HA6nVeAihMPhcDgcTqvARQiHw+FwOJxWgYsQDofD4XA4rQIXIRwOh8PhcFoFLkI4HA6Hw+G0ClyEcDgcDofDaRX+H3xcyJflaLU1AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import xarray as xr\n",
    "\n",
    "# 导入真实的自变量\n",
    "X1 = xr.DataArray((df['Label'] == 'Friend').astype(int))\n",
    "X2 = xr.DataArray((df['Label'] == 'Stranger').astype(int))\n",
    "\n",
    "# 基于后验参数生成y_model\n",
    "model1_trace.posterior[\"y_model\"] = model1_trace.posterior[\"beta_0\"] + model1_trace.posterior[\"beta_1\"] * X1 + model1_trace.posterior[\"beta_2\"] * X2\n",
    "df['Mean RT'] = df.groupby('Label')['RT_sec'].transform('mean')\n",
    "\n",
    "# 绘制后验预测线性模型\n",
    "az.plot_lm(\n",
    "           y= df['Mean RT'],\n",
    "           x= df.Label,\n",
    "           y_model = model1_trace.posterior[\"y_model\"],\n",
    "           y_model_mean_kwargs={\"color\":\"black\", \"linewidth\":2},\n",
    "           figsize=(6,4),\n",
    "           textsize=16,\n",
    "           grid=False)\n",
    "\n",
    "# 设置坐标轴标题、字体大小\n",
    "plt.xlim(-0.5, 2.5) \n",
    "plt.xticks([0, 1, 2]) \n",
    "plt.xlabel('Label')  \n",
    "plt.ylabel('RT (sec)')  \n",
    "plt.legend(['observed mean', 'Uncertainty in mean', 'Mean']) \n",
    "\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ArviZ 自带的绘图工具不够灵活和美观。 我们可以自己定义函数来绘制后验预测线性模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_prediction(df, predicted_y=\"prediction\", ax=None):\n",
    "\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(figsize=(5, 4))\n",
    "    \n",
    "    sns.boxplot(x='Label', y='RT_sec', hue='Matching', data=df, palette='Set2', ax=ax)\n",
    "\n",
    "    prediction = df.groupby([\"Label\", \"Matching\"])[predicted_y].mean().reset_index()\n",
    "    # 创建映射字典：Label到x位置\n",
    "    label_to_x = {'Self': 0, 'Friend': 1, 'Stranger': 2}\n",
    "    # 将 Label 映射到相应的 x 值\n",
    "    prediction['x_position'] = prediction['Label'].map(label_to_x)\n",
    "    # 根据 Matching 设置偏移量\n",
    "    prediction['x_offset'] = np.where(prediction['Matching'] == 'matching', -0.2, 0.2)\n",
    "    # 计算最终的 x 位置\n",
    "    prediction['final_x'] = prediction['x_position'].to_numpy() + prediction['x_offset'].to_numpy()\n",
    "\n",
    "    ax.plot(prediction['final_x'], prediction[predicted_y], marker='o', linestyle='', color='red', label=\"prediction\")\n",
    "    ax.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import xarray as xr\n",
    "\n",
    "# 导入真实的自变量\n",
    "X1 = xr.DataArray((df['Label'] == 'Friend').astype(int))\n",
    "X2 = xr.DataArray((df['Label'] == 'Stranger').astype(int))\n",
    "\n",
    "model1_trace.posterior[\"y_model\"] = model1_trace.posterior[\"beta_0\"] + model1_trace.posterior[\"beta_1\"] * X1 + model1_trace.posterior[\"beta_2\"] * X2\n",
    "\n",
    "df[\"model1_prediction\"] = model1_trace.posterior.y_model.mean(dim=[\"chain\",\"draw\"]).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prediction(df, \"model1_prediction\")\n",
    "\n",
    "# 显示图形\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到，当仅考虑“Label”条件时，由于没有考虑到“Matching”条件的影响，模型预测的 y 值与真实值存在较大的偏差。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## 模型二：2 X 3 的多元线性回归模型：无交互\n",
    "\n",
    "模型一仅考虑了“Label”对模型的影响。\n",
    "\n",
    "然而，反应时间可能不仅受到标签的影响，还可能受到匹配水平(matching)的影响。因此，第二个研究问题是：“**匹配条件是否会影响反应时间？**”。\n",
    "\n",
    "如果把“matching”条件加入到模型中，会不会让模型更好？我们来看看如何建立模型二。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 哑变量编码规则\n",
    "\n",
    "模型二加入了新的自变量“Matching”（matching， non-matching），我们先不考虑两个自变量之间的交互作用，即“Label”和“Matching”是独立的影响因素。在新的模型中，“Label”是一个三水平因子（Self、Friend、Stranger），而“Matching”是一个二水平因子（matching、non-matching）。\n",
    "\n",
    "因此，我们需要对两者分别进行treatment编码，然后将其合并为模型矩阵。\n",
    "\n",
    "**模型设计与编码规则**\n",
    "\n",
    "- Label (三水平因子): 采用 treatment 编码，将 \"Self\" 作为基线，生成两个对比列：\n",
    "    - Contrast 1：Friend vs Self\n",
    "    - Contrast 2：Stranger vs Self\n",
    "\n",
    "- Matching (二水平因子): 采用 treatment 编码，将 \"matching\" 作为基线，生成一个对比列：\n",
    "    - Contrast3 (matching vs non-matching)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "最终，模型矩阵将有：\n",
    "\n",
    "- 一个截距列（表示基线条件 “Self-matching” 的反应时间）。\n",
    "- 两个与 “Label” 相关的对比列。\n",
    "- 一个与 “matching” 相关的对比列。\n",
    "\n",
    "三个 $\\beta$ 参数对应了三种对比假设。即，假设 Friend 与 Self 的反应时间相同，Stranger 与 Self 的反应时间相同，nonmatching 与 matching 的反应时间相同。\n",
    "\n",
    "| Label    | Matching  | 截距 (baseline) | Contrast1 (Friend vs Self) | Contrast2 (Stranger vs Self) | Contrast3 (matching vs nonmatching) |\n",
    "|----------|-----------|-----------------|----------------------------|------------------------------|--------------------------------|\n",
    "| Self     | matching    | 1               | 0                          | 0                            | 0                              |\n",
    "| Friend   | matching      | 1               | 1                          | 0                            | 0                              |\n",
    "| Stranger | matching      | 1               | 0                          | 1                            | 0                              |\n",
    "| Self     | nonmatching  | 1               | 0                          | 0                            | 1                              |\n",
    "| Friend   | nonmatching  | 1               | 1                          | 0                            | 1                              |\n",
    "| Stranger | nonmatching  | 1               | 0                          | 1                            | 1                              |\n",
    "\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在模型二中，两个分类自变量$X$（Label：Self, Friend, Stranger） 和 $M$ （Matching：matching, nonmatching ）的关系可以表示为：\n",
    "\n",
    "$$\n",
    "Y = \\beta_0 + \\beta_1 \\cdot X_1 + \\beta_2 \\cdot X_2 + \\beta_3 \\cdot M_1 + \\epsilon_i\n",
    "$$\n",
    "\n",
    "通过Treatment 编码：\n",
    "- $\\beta_0$：表示基准条件（Self-matching）的均值；\n",
    "- $\\beta_1$：Friend 条件相对于 Self 条件的均值差异（在 matching 条件下）；\n",
    "- $\\beta_2$：Stranger 条件相对于 Self 条件的均值差异（在 matching 条件下）；\n",
    "- $\\beta_3$：nonmatching 条件相对于 matching 条件的均值差异。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "那么现在，我们有了$\\beta_3$，代表的是“matching”变量的斜率，因此我们也需要给$\\beta_3$设置先验分布：\n",
    "\n",
    "- $\\beta_0$： \n",
    "$$ \\beta_0 \\sim N(5, 2^2) $$\n",
    "- $\\beta_1$ 和 $\\beta_2$ ： \n",
    "$$ \\beta_1 \\sim N(0, 1^2), \\quad \\beta_2 \\sim N(0, 1^2) $$\n",
    "- $\\sigma$： \n",
    "$$ \\sigma \\sim Exp(0.3) $$\n",
    "\n",
    "**新增参数**\n",
    "- $\\beta_3$： \n",
    "$$ \\beta_3 \\sim N(0, 1^2) $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**完整模型设定**\n",
    "\n",
    "\n",
    "模型可表示为：\n",
    "$$ Y_i \\mid \\beta_0, \\beta_1, \\beta_2, \\beta_3, \\sigma \\sim N(\\mu_i, \\sigma^2)$$\n",
    "$$ \\mu_i = \\beta_0 + \\beta_1 \\cdot X_1 + \\beta_2 \\cdot X_2 + \\beta_3 \\cdot M_1 $$ \n",
    "\n",
    "先验分布：\n",
    "\n",
    "- $\\beta_0$： $$ \\beta_0 \\sim N(5, 2^2) $$\n",
    "- $\\beta_1$ ~ $\\beta_3$ ： $$ \\beta_1 \\sim N(0, 1^2), \\quad \\beta_2 \\sim N(0, 1^2), \\quad \\beta_3 \\sim N(0, 1^2) $$\n",
    "- $\\sigma$： $$ \\sigma \\sim Exp(0.3) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先验设置：\n",
    "\n",
    "* > $Y_i {\\sim} N\\left(\\mu_i, \\sigma^2\\right)$  \n",
    "\n",
    "* > $\\sigma   \\sim \\text{Exp}(0.3)$  \n",
    "  \n",
    "* > $\\beta_{0}   \\sim N\\left(5, 2^2 \\right)$  \n",
    "\n",
    "* > $\\beta_1   \\sim N\\left(0, 1^2 \\right)$  \n",
    "\n",
    "* > $\\beta_2   \\sim N\\left(0, 1^2 \\right)$  \n",
    "  \n",
    "* > $\\beta_3   \\sim N\\left(0, 1^2 \\right)$  \n",
    "\n",
    "  \n",
    "定义回归模型：\n",
    "* > $\\mu_i = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 M_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型拟合和推断\n",
    "\n",
    "我们可以通过 PyMC 构建该模型，并使用 MCMC 算法进行采样。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 转换分类变量为哑变量\n",
    "X1 = (df['Label'] == 'Friend').astype(int)\n",
    "X2 = (df['Label'] == 'Stranger').astype(int)\n",
    "\n",
    "# Matching 条件的哑变量\n",
    "Matching = (df['Matching'] == 'matching').astype(int)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "with pm.Model() as model2:\n",
    "    # 先验分布\n",
    "    beta_0 = pm.Normal('beta_0', mu=5, sigma=2)  # 截距\n",
    "    beta_1 = pm.Normal('beta_1', mu=0, sigma=1)  # Friend 的主效应\n",
    "    beta_2 = pm.Normal('beta_2', mu=0, sigma=1)  # Stranger 的主效应\n",
    "    beta_3 = pm.Normal('beta_3', mu=0, sigma=1)  # Matching 的主效应\n",
    "    sigma = pm.Exponential('sigma', lam=0.3)  # 误差项的标准差\n",
    "    \n",
    "    # 线性模型\n",
    "    mu = beta_0 + beta_1 * X1 + beta_2 * X2 + beta_3 * Matching\n",
    "    \n",
    "    # 观测数据的似然函数\n",
    "    likelihood = pm.Normal('Y_obs', mu=mu, sigma=sigma, observed=df['RT_sec'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**进行后验采样**\n",
    "\n",
    "接下来我们使用`pm.sample()`进行mcmc采样  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta_0, beta_1, beta_2, beta_3, sigma]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ee73a1b652ed40259391f040fca1220c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 4 seconds.\n"
     ]
    }
   ],
   "source": [
    "with model2:\n",
    "    model2_trace = pm.sample(draws=5000,                   # 使用mcmc方法进行采样，draws为采样次数\n",
    "                      tune=1000,                    # tune为调整采样策略的次数，可以决定这些结果是否要被保留\n",
    "                      chains=4,                     # 链数\n",
    "                      discard_tuned_samples=True,  # tune的结果将在采样结束后被丢弃\n",
    "                      random_seed=84735)           # 后验采样  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MCMC诊断和后验推断**\n",
    "\n",
    "我们可以使用 `az.summary` 函数来查看诊断和后验推断的摘要。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>beta_0</th>\n",
       "      <td>0.714</td>\n",
       "      <td>0.020</td>\n",
       "      <td>0.676</td>\n",
       "      <td>0.750</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12261.0</td>\n",
       "      <td>12412.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_1</th>\n",
       "      <td>0.064</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13935.0</td>\n",
       "      <td>13475.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_2</th>\n",
       "      <td>0.061</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.106</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13640.0</td>\n",
       "      <td>13998.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_3</th>\n",
       "      <td>-0.021</td>\n",
       "      <td>0.019</td>\n",
       "      <td>-0.058</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18922.0</td>\n",
       "      <td>14291.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.133</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.120</td>\n",
       "      <td>0.147</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18368.0</td>\n",
       "      <td>13132.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "beta_0  0.714  0.020   0.676    0.750        0.0      0.0   12261.0   12412.0   \n",
       "beta_1  0.064  0.024   0.018    0.109        0.0      0.0   13935.0   13475.0   \n",
       "beta_2  0.061  0.024   0.016    0.106        0.0      0.0   13640.0   13998.0   \n",
       "beta_3 -0.021  0.019  -0.058    0.015        0.0      0.0   18922.0   14291.0   \n",
       "sigma   0.133  0.007   0.120    0.147        0.0      0.0   18368.0   13132.0   \n",
       "\n",
       "        r_hat  \n",
       "beta_0    1.0  \n",
       "beta_1    1.0  \n",
       "beta_2    1.0  \n",
       "beta_3    1.0  \n",
       "sigma     1.0  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(model2_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 ROPE+HDI 对参数进行检验\n",
    "\n",
    "- 可以看到，$beta_3$ 非常接近0，表明该参数没有显著性。 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yd67uE8Ch9GL+uTq+HSIUouWkYy+sVnZJFTM+3MZnO1II8XTky7uH8eac/ng42bW6rTmDQgn1cuS7fekk5ZW3Q7RCCNFx6rQ6w0nos1Nim91fP0x/+a7Udo1LCCE6SkF5DR9vTcLd0ZZ7xka1qQ2VSsUbs/sR6uXIJ1uTWH8828RRCtFy0rEXVqmipo55S3aTkFPG9YNCWPP42Fbdpb+YnY2ax67ojlan8N76UyaMVAghOt63e9M5nVvOzLhg+gS7N7v/pF7++Lra88uhTEqqajsgQiGEaF9f7U6lokbL3aMjcXdsut5Sc9wdbVl080Bs1Cr+9uMRiislRwrzkI69sEqv/n6C+KxSZsUF8+b1/XCys7nsNmfGBRPl68zPhzI5k1tmgiiFEKLjVdTU8c76U9hp1Dw5uXuLXmOrUXPTkFAqarT8fCCjnSMUQoj2VavVsWxHCvY2am5tYcG8S+kf6sG9Y6PILa2WIfnCbKRjL6zO8cwSvtqdSri3E6/N6tuqQiiXolGreHB8DIoCi/88Y5I2hRCio33yZxK5pdXcPiKcUC+n5l9wzk1Dw1Cr4MtdqSiK0o4RCiFE+1p9NIuskipmDAjGy7n1UzQb8+gV3YjwdmL5rlSOpBebpE0hWkM69sLqvPfHKRQF/nZ1LA62GpO2Pb1/EEHuDvywL4PsElnaRAjRuRSU1/DfLWdwc7Dh4YkxrXptsIcjE3r4EZ9Vyv7UwnaKUAgh2t/Xe+rrhcwbGWGyNh1sNbxwTS8AuWsvzEI69sKqpOZXsPZ4Nt39Xbiqd4DJ27ezUXP3mChqtDqWbJWln4QQnctHm09TVl3HfeOi21RI9NbhYQB8uVOK6AkhOqezxZVsP51P7yA3egW5mbTtST39GBLhydbEPLacyjVp20I0Rzr2wqp8uSsFRYE7R0WabAj+xW4aGoqnky1f7EyhuEIKpAghOoes4io+256Mj4s9d46KaFMb47r7EezhyG9HzlJYXmPaAIUQogP8cjATRamvnWRqKpWK566uX2nkw42yRLLoWNKxF1ZDq1P4+WAmjrYapvcParfjONnZcMfISMprtCzbmdxuxxFCCFP6YEMC1XU6Hp4Q3eaCohq1ipuHhlJTp+OH/ekmjlAIIdrfjwcyUKtg+oD2OVccFO7FkAhPdiUVyFx70aGkYy+sxq4z+WSVVHFVb3+c7S+/Cv6l3D4iHEdbDZ/vSKFWq2vXYwkhxOXKKq7i271pBHs4cvOwsMtq64bBodioVVJETwjR6STmlBKfVcrobr74uTq023HuGh0FwCdbpdiy6DjSsRdWY/WxLKD9rsBeyNPZjhlxQeSUVrPueHa7H08IIS7H0u1J1GoV7h4Tib3N5RUV9XNzYHIvf5LyytlxOt9EEQohRPtbc6z+nO3qPqavw3Shyb38CfNy4rfDZ8ktrW7XYwmhJx17YRUUReGPEzk42moYGe3TIce8dVj9uqfLdqR0yPGEEKItSqtqWb4zFXdHW24YHGqSNvX578tdUkRPCNF5rD6ahUoFk3r6t+txNGoVNw4JpU6n8PPBjHY9lhB60rEXViE+q5SMokpGd/Mx+RJ3TekT7E5cmAc7zuSTmFPaIccUQojW+n5fOqXVddw2PNxk05RGRnsT4e3EmmNZ5JTK0p9CCMuXUVTJkYxiBod74utq3+7Hmz0wBLWqPgcL0RGkYy+swh8n6odWTerp16HHvW14/V2rL2TpJyGEBVIUha93p6FWnV+qzhTUahU3DQ2jTqfwy8FMk7UrhBDtZd25KZvtsRxyYwLcHRjdzZf4rFKOZUoRPdH+pGMvrMKG+BwAJsS2b8d+586dTJo0CVdXV9zd3fnfC/dgW5TKb4czqWthEb2L25g6dSqHDx9ucv/jx49zyy23EBgYiL29PSEhIcycOZPs7Kbn9ldUVBAVFYVKpeLxxx9v7dsUQliJQ+nFnMwuZVx3XwLdHU3W7s6dO/ly/j2kvjOHB67s12wea6qN9siF//3vf7nlllvo0aMHarUaDw+PtrxFIYSV2Xiyfl35K9p5GD5AdXU1L774ImtevJ6Ut2YydnBfXn/9derq6lrdRmRkJA4ODsTExDTaRkZGBq+99hpjxowhICAAe3t7YmJiePbZZyktbTii9OTJk/z1r39l/PjxuLm5oVKpePfddy/3LQsL0L6lw4XoABU1dRxOLyY2wLVdK5zu3LmT8ePHExwczMsvvwzAokWLSN/8NN63vMnWxP6M73HpCwtNtTF69Gh27txJr169jPZfs2YNM2bMoHfv3jzxxBP4+PiQnZ3Njh07KCkpwd+/8S+nBQsWkJuba4J3LYTozL7ZUz+a6MYhpplbD8Z5rN/0e0gtqODYiT+azGPNtWHqXPj6669TUFDAwIEDKSkpobKy0mTvXQjROVXVatl5Jp9wbycifZzb/Xg33ngjP//8M7fPu4M1eW4o2ad4/vnnOX36NB9//HGr2vjLX/7CiBEj2LFjR6Nt/PrrryxYsICpU6cya9YsnJyc2Lx5M2+++SarV69m586dODqev7C7Y8cO3n77bWJiYoiLi2PLli0mf//CTBQhOrltiblK+LO/Kf/345F2Pc7QoUMVV1dXJT093bAtPT1dcXJ2URyiBimPfbW/zW24uroqV199tdG+2dnZipeXl3LbbbcpWq22xXEeOnRIsbGxUd58800FUB577LEWv1YIYT2qauuUPvNXK3Evr1Wqa1ueQ5pzYR77fEeyEv7sb8qCr7c0msda0oaeqXJhUlKSotPpFEVRlHHjxinu7u4tf3NCCKu0MT5bCX/2N+XFn9r3XFFRFGXlypUKoDz55JOKoijKfZ/vVcKf/U257Z6HFEDZtWtXq9vQe/LJJxu0cfToUeXs2bMN2njxxRcVQFm0aJHR9vz8fKWoqEhRFEXZuHGjAijvvPNOa9+msEAyFF+0yKeffopKpWL9+vW89NJLhIWF4eTkxLhx4zh+/DgA33//PQMGDMDR0ZFu3brxww8/NGjnq6++YuTIkbi4uODs7MzYsWNZt25dg/3+/e9/M3nyZIKCgrCzsyMkJIT77ruPvLw8o/2Sk5MZFeNL0dYv0aXsZeDAgTg4OBAaGsprr71msvd/+vRpdu/ezZw5cwgODjZsDw4O5sYb5lCVdICVe09RUdP0EKtLtTFnzhzWrFlj9P4++ugjSkpKWLhwIWq1mvLy8maHcOl0Ou69914mTZrE9ddffxnvWAjRGEvOhSqVipdeeolffvmFgQMH4urszIm35+IW/yt2Nqb5ur84j13TNxCNWsX2s0qjeawlbeiZKhdGRESgUqku/80KIZrUmXKhg4MD143uR/GObxnfw7d9fiEXWL58OYBhKuTVfevn9AeNng3Al19+2eo29PSPL2yjd+/eBAQ0rBswZ84cAI4cOWK03cvLC3d392ZjEJ2PdOxFqzz33HOsXr2ap556iueee479+/czZcoUPv/8cx5//HHmzJnDG2+8gU6n48Ybb+T06dOG177wwgvccsst+Pj48I9//IN//OMfVFZWMmXKFH788Uej47z11lv4+/vz+OOP88EHHzB16lSWLl3KhAkTqKmpaRBX5Zm9LH7tWaZPn87ChQsJCwvjhRdeYNmyZUb7lZWVkZeX16J/FRUVhtft2bMHgBEjRjQ49ogRI0DRUZx26pJr2l+qjeHDh6PT6di/f79h28qVK4mNjWXHjh3Exsbi4uKCg4MDEydO5MCBA40e49///jeHDh1i0aJFTcYhhLh8lpoLV65cyb333sv06dMZO/cJbNx82bz8g3bLhV7OdgwK9yQ+q5TYfgMb5LHGdEQuFEJ0jM6QCxcuXAguPhRt+ZwzO1YZ7dfWXHgpe/bsITg4mNDQ+ilQE2P9sLNRsyMbgoKCDDmwNW3ohYaGtriN9PT6avy+vu1/MUNYCHMPGRCdw9KlSxVAGTJkiFJbW2vY/u9//1sBFDc3N6MhlYcOHVIA5dlnn1UURVH27dunAMr8+fON2q2trVUGDx6shIeHG4ZOKoqilJWVNYhhyZIlCqB88803hm0JiacVQFHbOijJycmG7RUVFYqvr68ybNgwozbmzZunAC36d2Gsb731lgIoK1eubBDX77//rgCK99WPKg98sbfJ32FL2vjkk08M2zw8PBQvLy/FxsZGeeihh5QVK1Yo//znPxU3NzfF2dlZOX78uFEbGRkZipubm7JgwQJFUeqHoyJD8YUwKUvNhfq/dycnJyU5OVmpqdMq/V5ao/T7v1/aPRf+Z1OiEv7sb8pTC5c2yGONae9ceCEZii9E++gsuVBRFCU1v1wJffIHxd7V02S58FJcXFyUoUOHGm2769M9Svizvyl9BgxUQkND29SG3pAhQ5pto66uThkxYoSi0WiUY8eONbmfDMW3LlI8T7TKfffdh43N+Y+N/o7L9OnTjYZU9uvXDzc3NxISEoD6IUMqlYq5c+c2GDY1bdo0XnrpJRISEujevTsAzs71hU10Oh0lJSXU1dUxfvx4AHbt2sUNN9wAwOncMgC6DZ1AeHi4oU1HR0eGDx/O9u3bjY71zDPPMHfu3Ba916ioKMPP+qu09vYN1z11cKgv2Oei0bH5ZC7VdVrsbTQN9mtJGxdeDS4tLUWr1fK3v/3NaFrBoEGDmDRpEgsWLODrr782bH/kkUfw9/fn2WefbdH7E0K0naXlQr2ZM2cSHh7Onwm5FFfWctOQcI63cy68ItaPN1bFczSrwmifprR3LhRCdBxLz4UAm07lora1p0ffgSSePGi0X1tz4aVUVFQ0yG9T+waw/kQ25XXqFt35b6wNPQcHh2bbePbZZ9mxYwcvvvhiiwqaCusgHXvRKhEREUaP9csIXbwdwNPTk4KCAgBOnDiBoih069atybazs7MNCXzdunW8/PLL7Nmzh+rqaqP9CgsLDT8fTq9fFzS2e0yD9ry8vMjPzzfa1qtXrzYlOP3J5sWxAFRVVQHQJ9yHozVadpzOb7Q6fkvauLBqqYODA+Xl5dx5551G+15xxRWEhYWxceNGw7Zff/2VFStWsHbt2ia/CIQQpmNpuVAvMjISgE0XLOuU1c65MMbPhVAvR47srz85vzCPtbQNvcvNhUKIjmXpuRBg87l8GB3iz+HtpsmFBQUFDaYA6Oe5Ozg4NIjxip7+2GpUZBeX4d5MjmyqDb2qqqpL5tnXX3+dhQsXctttt7FgwYJmjyWsh3TsRatoNA3vRF9qu6IoQP0VVo1Gw6pVq5osatSnTx+g/srr1VdfTY8ePXjzzTeJiIjA0dERrVbLlClT0OnOrxd/KL0IgFCvli1dUlxc3OKlj1xcXHBxcQEgJCQEqF8r9GL6bWMHxHI0EdafyG60Y9+SNvT7QP08qvj4eAIDAxvsHxgYaDQH9aGHHmLixIlERkaSmJho1GZxcTGJiYn4+vpKsRQhTMTScuHFx998KhdbjYoR0d40VqbJlLlQpVIxsYcfxzfkGu3TlPbMhUKIjmXpubCmTsf203kEujvg5mjbYL+25sJZs2axefPmRt9bSEhIg/zm7mjLiGgflhfmEN0jutljNdaGXkZGBmFhYY0+9/bbb/P8889zww03sHTpUikk2sVIx150iG7durFmzRoiIyOJiWl4d/1CX3/9NVqtlt9//93oiu/JkyeN9lMUxXDH3svZrkVxPPbYY3z22Wct2nf+/Pm89NJLAAwePBioX/vz7rvvNtpv586dqNVqbrlmHJ/95yAbTuSgXKc0SKYtaWPgwIGGbUOHDiU+Pp60tDR69uxptH9aWhp+fn5Gj9PS0hq98v3pp5/y6aef8sEHH/Dwww+36L0LIdpHe+TCi2UWVZKYU8bwKC9c7Bv/mjd1LhwV48PCzJOoLspjjWnPXCiE6Bw6IhcC7E0poKJGy/T+QWQ1sntbc+HChQsbHSkA9Tlu+fLlpKWlGRW/G+hVx7KyAjzCrmn2WE21kZaWRmZmJrNmzWrwmkWLFvHUU08xc+ZMvvzyyyYvrgjrJR170SHmzp3LokWLeOGFF/jqq69Qq40XZMjJyTGcnOnnaumvfOq98cYbRo9TCyooKK8fBtXSK5JtnUvVrVs3Bg0axHfffccrr7xCUFAQAJmZmXz33XdMnjyZkMAAhkd580d8DofPZGJfW4qPjw8+Pj4tbuPCyqW33XYbn3/+OR9++KFRlfsff/yRzMxM7r33XsO27777rkH8ubm5PPjgg1xzzTXccccdxMXFteh9CyHaT3vkwottOVV/53xs96YrIZs6F4Y5VFNxcis+3Qcb5bHi4mLOnj3bYblQCNE5dEQuBPgzoX6K0NjuvnzbyPNtzYWDBg1qcr+bb76Z5cuX8+6779ZX5D/nxPpvAFDHjDHa//Tp09TW1hIbG9tsG++++y4At956q1Ebixcv5tFHH2XatGl88803RnUPRNch/9dFhxg2bBgvvvgir7zyCqdOnWL27NkEBASQkZHB9u3bSUxMNCyBMmPGDN5++22mTp3Kfffdh1qt5tdff21wZXRPcuNXSi+lrXOpAN5//30mTJjAmDFjeOSRRwD44IMPUBSFt956C4CRMT78EZ/Dh0u/YvE/nja6utvSNvQmTZrEzTffzIcffkhOTg4TJ04kMTGRRYsWERgYyPz58w37NrZmfXJyMgAxMTGypr0QFqI9cuHFtiSc69h3a7pj3x65UK0C21G3U1RRg4dT/SiqH3/8kTvvvLPDciHU1xw5dOgQACkpKVRXV/Pqq68C9fN/ZeSSEObXEbkQ6i90qlUwKtqn0Y795eTCpkybNo1p06bx9ttvU1xczIgRI9ixYweffPIJwUOvJkkTREF5jWG06RVXXEFKSorRhYtLtXHHHXcwfPhww76//PIL9913H15eXsyYMYNvvvnGKB5/f38mT55seFxcXMwHH3wAQFJSElBfw6CsrL4g9fTp0+nXr59Jfyeig5ihEr/ohPTLmmzcuNFou35ZkcaWAAkPD1fGjRtntO2nn35SJk6cqLi7uyv29vZKeHi4ct111ylff/210X7fffed0r9/f8XR0VHx8/NT7rrrLiUvL08BlHnz5imKoijPfHdICb7/kyaPr1/CxJS2bdumTJgwQXF2dlZcXV2VKVOmKAcOHDA8H3+2RAl/9jdl/D3zm4yruTYuVFtbq7zxxhtK9+7dFVtbW8XX11e57bbblNTU1GZjleXuhDA9S8yFFx7/xRf/rvSZv1oZ9Mo6RautXyqqo3Lho4tWKOHP/qasOpJp2E//++rIXHip5avCw8NN9BsQomuz9Fw4f/58JaekSgl/9jdlxodbFUVpn1zYlMrKSuX5559XwsLCFDs7OyUqKkp59dVXlTdXHlXCn/1N+X5vmmHf8PDwRuNqqo2amhqj/ebPn3/JZfou/p3rf0dN/Vu6dGl7/EpEB1ApykXjWoToJCYu3ER6YSVHXrqy0eXlzEFRFIb84w9qtTr2vzgZjVqKlgghOs6+lEJm/2c7s+KCefvGAR167K0Jecz9ZBe3DQ/nlRl9OvTYQghxsR8PpPPEN4d47IpuPDG5u7nDAeBoRjHTPtjK1X0C+M/cpofzC9EW6uZ3EcLy5JdVcya3nAEhHhbTqYf6uf4jo70prqzlWGaxucMRQnQxO8/UL+U0Msanw489OMITOxs1207nNb+zEEK0sy2nzs+vtxS9g9wIcHNg86lcqmq15g5HWBnp2ItOaW9K/byqIZGeZo6koRHR3kDbagAIIcTl2J1Uv0b0sEivDj+2g62GQWGenMktJ6u4qsOPL4QQejqdwp8Jubg52NA/xHKW+lWpVEzq5UdFjdZwIVYIU5GOveiU9pw7eR0c0fEnr80ZFF5/sWF/qnTshRAdp06rY29yAUHuDoR4OpolhpHnLmxul7v2QggzOn62hLyyGkZ388FGY1ndnUk9/QFYfyLbzJEIa2NZn3QhWmhPSiEqFQwMs7w79jG+Lrg62LA/RTr2QoiOc/xsCeU1WoZFebd4CVBT008B2JYod6KEEObTktVBzGVEtDfOdhrWH89psISfEJdDOvai06moqeNYRjE9/F1xd7Q1dzgNqNUq4sI8OVtcRWZRpbnDEUJ0EbvO1I9kGmqGYfh6/UPccbG3YfvpPDlhFUKYzZZT5zr2FjS/Xs/eRsPY7r5klVRxLLPE3OEIKyIde9HpHEwrok6nmPXktTmDzo0k2Cd37YUQHWSXGefX69lo1AyL9OJscRXJ+RVmi0MI0XWVV9exL6WQGD8XgjzMMy2pOTIcX7QH6diLTmdPUn1n2RLn1+vp59lLx14I0RF0OoU9yQX4utoT6eNs1lj0BUR3nJbh+EKIjrfjdD61WsUih+HrTYj1Q62Sjr0wLenYi05nb0r9XakhEZY3v16vf6g7ahUckAJ6QogOcCqnlOLKWoZGepltfr3e8KhzHXup+CyEMAN9Z3lCrOV27L2c7YgL8+RoRgk5pbKKiDAN6diLTqVOq2N/SiHBHo4Eulvm8CoAVwdbuvu7ciyzhMoaWadUCNG+9qcUATA43PwXPHsFuuHuaMuO0/kyz14I0aF0OoX1J3JwtbdhWKS3ucO5pPHn5v9vPplr5kiEtZCOvehU4rNKKa/RWvT8er2B4Z7U6RSOZhabOxQhhJU7mFY/OijOAlYKUatVDIv0Iq+smtO5ZeYORwjRhRxIKyKvrJrxsX7Y2Vh2N2dCrB8Am05Jx16YhmV/4oW4yG7D+vXmP3ltTr9gdwCOpEvHXgjRvg6kFmGnUdMz0NXcoQAXrmcvw/GFEB1n3fH6YfiTe/mbOZLm9Qp0w8fFnj9P5VKn1Zk7HGEFpGMvOpXz8+st/45935D6jv3RDOnYCyHaT0lVLYm5ZfQOdsPeRmPucAAYEV2/nr0U0BNCdKR1x7Ow1agY38Ny59frqdUqxnX3paSqjgNpReYOR1gB6diLTkNRFPYkF+LuaEuMr4u5w2lWd39X7GzUHJaOvRCiHR1OK0ZRYECoh7lDMeju74K3sx07z+Sj08k8eyFE+zuTW8bp3HKGR3nj5mBr7nBaRF/gb2N8jpkjEdZAOvai00gtqCC3tJohEZ6o1eat+twStho1PQPdOJ1bRll1nbnDEUJYKf3qG5Ywv15PpVIxPMqbwopaTmaXmjscIUQXoK+G3xmG4euNifFFrYJNUkBPmIB07EWncX5+veUPw9frF+yOosDxzBJzhyKEsFIHzw3hjLOgO/YAw2U9eyFEB9LPr5/Us/N07N2dbBkY5snxsyVkl8iyd+LySMdedBp7k+vvSlny+vUX63uugN7h9CLzBiKEsEqKonAgrQgfFztCPC1rCdARsp69EKKD5JdVsy+lkN5BbgR5WFYubM64c8vebU3IM3MkorOTjr3oNPakFGBno6bPuc5yZ6AvoHdE5tkLIdpBakEFBeU1DAj1RKWyrClK0b7O+Lras+tMPlqZZy+EaEd/xOegUzrXMHy9kTH1xUa3nZaOvbg80rEXnUJ+WTVncssZEOphMVWfW6Kbnwv2NmpZ8k4I0S4Mw/DDPMwaR2NUKhUjorwpqarjxFmZjiSEaD+daZm7i/UPccfF3oYdp/NRFLkIKtpOOvaiU9jTCYfhA9ho1PQOcuNMXjmlVbXmDkcIYWUOpBYBlje/Xm+EzLMXQrSzyhotfybkEuzhSK9AN3OH02o2GjXDIr04W1xFUl65ucMRnZh07EWnsDe58xXO09PPsz+aIXeshBCmdSCtCJUK+llqx17m2Qsh2tnWxDyqanVM7uVvcVOSWur8cHzJlaLtpGMvOoU9KYWoVDAovHPdsQfoG+IBwJGMIrPGIYSwLlW1Wo5nFtPdzxUXextzh9OocG8nAt0d2J1UQJ1WZ+5whBBWaH0nHoavN/Lc6KbtiTLPXrSddOyFxauoqeNYRjGxAW64OdiaO5xW62cooCd37IUQpnMss4RarWKR8+v19PPsy6rrOCrLfgohTEyrU/gjPhs3BxuGRna+UZ16Pfxd8Xa2Y8eZfHRSbFS0kXTshcU7mFZEnU7pdPPr9aJ9XXC01ciSd0IIk9IXzhtgocPw9fTr2W+Xis9CCBM7mFZIXlkNE2L9sNV03m6NWq1iRLQ3RRW1HJdio6KNOu9fgOgy9iTVF87rjPPrATRqFb2D3EjJr6C4QgroCSFM40BqfW6MC7Psi56GefYyd1QIYWJrrWAYvt6oc/Ps5SKoaCvp2AuLtzelvnBeZ71jD9DPMM9elr0TQpjGwbQiXOxtiPFzMXcolxTq5USIpyN7kwupqZN59kII0/njRA62GhVju/uaO5TLNipa37GXi6CibaRjLyxanVbH/pRCQjwdCXR3NHc4baafZ39YCugJIUwgp7SK9MJK+oW4o1FbfhXoEVHeVNZqZUqSEMJkUvLLScwpY1ikd6eswXSxUC9Hgtwd2JtcKMVGRZtIx15YtPisUsprtAzppMPw9Qwd+zS5Yy+EuHwH9evXW3DhvAvJevZCCFPbEJ8DwMRYPzNHYhoqlYrh54qNHpNio6INpGMvLNruJP369Z13GD5AhLczrvY2crdKCGES5wvndY7caOjYy3r2QggT0Xfsr+hpHR17gOHnapLslFwp2kA69sKi6efXD+3kd+zVahV9Q9zJLK4it7Ta3OEIITq5A+fu2Ft6RXy9QHdHIn2c2ZdSSHWd1tzhCCE6ubLqOnaeySfa15lwb2dzh2Myw6Lqz3elYy/aQjr2wmIpisKe5EI8nGyJ9rXs4lAtcb6AXpFZ4xBCdG5ancLh9CJCvRzxdbU3dzgtNjzKm+o6neGihBBCtNXWhFxqtQpX9Oz81fAvFOblRKDMsxdtJB17YbFSCyrILa1mcLgn6k5QHKo5hnn26TLPXgjRdgk59bVHOsswfD2ZZy+EMJU/TljX/Ho9/Tz70uo6Wc9etJp07IXFOj+/vnMPw9eTjr0QwhT0d7zjOskwfL3h54aYyjx7IcTl0OkUNp7Mwc3BhkHhnesCZ0sMl+H4oo2kYy8s1t7kQoBOXxFfL9jDES9nOw6nF6EoirnDEUJ0UvqK+AM6SUV8PT9XB6J9nTmYWiTz7IUQbXY4o5i8shrG9fDDVmN9XZlhkfoCegVmjkR0Ntb31yCsxp6UAuxt1PQJdjN3KCahUqnoF+JOXlkNZ4urzB2OEKKTOpBWiJ1GTe+gzpcbB4V7UqPVyVJOQog223AiG4BJVlQN/0Lh3k4EuDmwJ6kArU5uBImWk469sEj5ZdWcyS2nf6gH9jYac4djMv2C9cPxi8wbiBCiUyqtqiUhp4xeQW6dMjcODKsfNisF9IQQbbX5VC4qFYzt5mvuUNpF/Tx7r/p59nIRVLSCdOyFRdpjGIZvXXOn9JXxZZ69EKItDqcXoyidZ5m7i8Wd69jvTy00cyRCiM6oqKKGwxnF9Alyx9PZztzhtBtZz160hXTshUXad279+sHh1jG/Xq9faP0d+0Nyx14I0QYHznWI4zrZ/Hq9bn4uuNrbGOoECCFEa2w/nY+iwOhuPuYOpV1Jx160hXTshUXaf+6kTz9s01r4uToQ7OHIwdQimTclhGi1g2lFAMR1sqXu9NRqFf1DPcgoqiS7RGqNCCFaZ2tiHgBjYqy7Yx/u7YS/mz27ZZ69aAXp2AuLU1On40hGMdG+zrg72Zo7HJOLC/OgvEbLqexSc4cihOhEFEXhQGoR3s52hHo5mjucNht4brTBARmOL4Ropa0JeTjYqhlkZVM1L3bhevYnZD170ULSsRcW51hmMTV1OqtcmxTOj0KQOaZCiNZILaggv7yGuDAPVCqVucNps/Pz7IvMG4gQolNJza8gtaCCoZHenbJ4aGvJcHzRWtKxFxbHWofh6w08d8Fif0qReQMRQnQq+w3z6zt3boyTO/ZCiDb4MzEXsP5h+HrSsRetJR17YXH2p9Sf7A200jv2vQLdsLdRy0mtEKJV9p3LjZ19NJOHkx1Rvs4cTq8fnSWEEC2xNaF+fr21F87Tizg3z36XzLMXLSQde2Fx9qcW4upgQ4yvi7lDaRd2Nmr6BrtzJq+cwvIac4cjhOgk9qcUoVGr6H9u2czOLC7Uk+o6HfFZMndUCNE8rU5h++l8fFzs6OHvau5wOoRKpWJYpDelVTLPXrSMdOyFRTlbXMnZ4ioGhHqgVnfeOaTN0Y9GOJAmd+2FEM0rq64jPquEXoFuONp1/rmlA8M9gPMjtIQQ4lJOnC2huLKWEdE+Vn1+eDEZji9aQzr2wqLo55139qGmzdFXhZZ59kKIljiUVoROsZ7cOCDUAzi/fJ8QQlyKvmM7PMrLzJF0LP373XmmwMyRiM5AOvbCoujnkFpr4Tw9qYwvhGgN/Z1tfeG5zq6HvyuOthrp2AshWmR3Un3Hdlikt5kj6ViRPs74udqzOylf5tmLZknHXliU/amFqFQwwEpOXpvi5+ZAsIcjh9KKJFELIZq1L9U6Cufp2Wjqa40k51dIrREhxCXpdAq7kwvwcbEj2tfZ3OF0KJVKxbAob0pknr1oAenYC4tRVavlWGYx3fxccHOwNXc47W5guCflNVpOZpWaOxQhhAXT6RQOpBbh52pPsIejucMxGf0F3IPpRWaNQwhh2U7llFJUUcvQSC9Uqq4zv15PPxx/V5IMxxeXJh17YTGOZZZQq1Wsfhi+nmGevQzHF0Jcwpm8MooraxkU7mlVJ7WGefapRWaNQwhh2Xad6ZrD8PWkgJ5oKenYC4tx+Nxdm/7nTvasncyzF0K0hL7IprVd9JQCekKIljDMr+9ihfP0onyc8XW1Z3dSATqZvikuQTr2wmIcSS8GoG+wu5kj6Ri9gtxwsFVzQO5WCSEuwVBU1Erm1+sFujvg52rPofQiFEVOVoUQDSmKwq6kfDycbOnu1zXWr7+YSqVieJQ3xZW1nMiSefaiadKxFxbjcEYxdjZqegR0jcRtq1HTL9iDpLxyCqR4lBCiCftSC7HTqOkT7GbuUExKpVIxINSDoopakvMrzB2OEMICnc4tJ6+shqERXl1q/fqLDYuUZe9E86RjLyxCWXUdp3PL6BXohq2m63ws48I9gPNLWQkhxIXyy6pJzCmjb4g79jYac4djcnHnphcckClJQohG7Eqqn1c+NLJrDsPX08+z3yXz7MUldJ0elLBoxzKKURToF9I1huHryTx7IcSl6OeWjoiyzqJRMs9eCHEp+sJ5w600B7ZUtK8zPi727JJ59uISpGMvLMKRjK41v14v7lxlfJlnL4RozI5zd2es9aS2X4g7apV07IUQDSmKwu6kAlwdbOgZaF1TkVqrfp69F8WVtcTLMsmiCdKxFxbh8LnCef1CPMwbSAfzc3UgxNORQ+lFaOUKrBDiIjvP5GOrUTHw3LQda+Nsb0N3f1dOnC2hqlZr7nCEEBYktaCCrJIqhkR4oenC8+v1hsmyd6IZ0rEXFuFIRjGOthqifZ3NHUqHiwvzpKJGy6lsuQIrhDgvr6yaU9ll9A/xwMnOxtzhtJsBoR7UahWOZUq1ZyHEeefXr+/a8+v1Rpxb7k9fd0CIi0nHXphdcWUtSXnl9A5yw6YLFc7TG3huOL7MsxdCXEg/v95ah+HryTx7IURjdp7rwA6z8hzYUtG+Lvi42Mk8e9GkrteLEhbnmH5+fRcrnKd3vip0kXkDEUJYlB2n609qR0Rb90ntgHMXN6VjL4S40O6kApzsNPQO6trz6/VUKhXDorwpqqjlpIzyFI2Qjr0wu8MZ+vn1XbNj3yvQDTsbtdyxF0IYMcyvP3fxz1p183PF2U7DwTTJgUKIeplFlaQXVjIo3LNLLYPcnOEyz15cgvylCLM7nF4EQN9gD7PGYS52Nmr6BrtzJrecoooac4cjhLAAeWXVJOSUMSDUA0c761u//kIatYq+Ie6kFVSSV1Zt7nCEEBZgT3L9VKQhETK//kLDz9UbkI69aIx07IXZHU4vxtlOQ5RP1yucpxd3bo7pARmKKoSg663dPCC0flTCQZmSJIRAOvZNifGrn2e/W+bZi0ZIx16YVUF5DemFlfQJdkfdhZcyGRgu8+yFEOfttPL16y8mBfSEEBfak1SIrUZlyA2inkqlYnC4F4UVtZzOLTN3OMLCSMdemNURM82v35O1h76f9aXvZ3256vurOvTYjYk7VzzqgMyzF0IAO87kY6dRt/v8ekvJhXFSQE8IcU7xueJwfYLdzTYVyVJyY2OGnBuOv/vcqAYh9Kx3YVxhJL4gnnUp6ziQc4CM0gzyq/JRq9SEuoYyKWwS83rPw8nWyeg1dbo6vj/1PauSVpFYlEh5bTl2GjuCXYIZFTSKO/rcgY+jT4tj2JO1h8+Pf87h3MOU1JTgbueOu6oHavvB9A2JM9o3pSSFt/e+zcHcg9Tqaunl3YsnBj5Bb5/eRvsdyzvGrStvZXTwaBZdsajtv6B2kFGWwZQfpjTYbqO2wcvei57ePbmhxw2MDRlLoLsjge4OHEwtQqdTUKtVVNZVsiJhBRtSN5BQmEBpbSnOts5EuEUwNmQsN/a4EXd74wsie7L28Jc1f2lwTI1Kg7u9Oz29ezKn+xyuCLui2Tgv5GrryvZbtrfxNyGE5civzOfDgx9yLP8YWeVZlNSUYKOywc/Jj4H+A5nXax4xnjFGr/ni+Bf8mfEnZ4rPUFxdTK2uFnc7d7p7dufa6Gu5NvraFh8/oyyDr058xZG8I5woOEFlXSUAQc5BrLl+DQC5pdUk5pQxNMKLnKp03t7aNXJhkLsDh9LO50A9yYVCdIy8yjw+OfIJf2b8ydmys9hqbIn2iGZ2t9nMiJmBWmV8P9CUuRGgoraCz459xopTK3HpkUGKxobbV8VyfffruTbqWlSq83mhq50nXmhohH6e/Vlw2yq5URioFEWRCRpdwMs7Xua7U981+XyMRwzLrl6Gi52LYduTm55kXcq6Jl/j7+TP99d+j4eDR7PHX3Z8GW/ueROFhh83Rafh70Pf4Ibe9UmjoraCWb/MIqMsg1dGvYK7nTvPbHkGW40tP07/EX9nfwC0Oi03/34zySXJ/HzdzwS6BDYbh15pTSkJhQkA2GvsG3wRmEJLEiHAyyNfZma3mTz45T5WHsli3RNjUdvn8MiGR0grTWvydV4OXrwz/h0G+g80bGsqYV9sXq95/HXIX1scpyRsYS3iC+KZ8+ucJp+319iz5Kol9PPtZ9h2/S/Xc7LwZJOvua3XbTwz5JkWHf+P1D94fOPjDbZf2LH/7XAmDy8/wAPjg9lY/lyXyYXd1H9h/7HurH9yLDF+rgCcLjotuVCIDpBcnMwdq+8gv6rxomxXR17NP8f806hzbcrcWFxdzF1r7mqyvZkxM3l51MtA1z1P1KvT6uj/2jI0QZ+i2OQ1+TrJjV2P3LHvQtzs3JgePZ0hAUOwUdvwc+LPrE1ZC0BiUSJfnPiC+/vfD0BqSapRp/6evvcwNHAopwpO8c6+d6hT6siuyGZN8hpujL3xksfNKMvg7X1vGzr183rNY2TQSLZnbuez45+hUmt57/ArTI4ehqeDJwdzD5JRlkE3z27MiJkBwPDA4WxK38TWjK3M7j4bqL9YcKLgBH8d/NdWJWsAVztXo0TXEZ4b+hyxXrFklmXy7v53yanIAWDJ0SXM7DaTgWGerDySxdYzKSzPeIKs8iygPjHf2+9eYjxiyCjL4H+H/0dGWQYFVQU8/MfDfD3ta8Lcwho95sJxC/Fx9KGwqpAlx5ZwOPcwAJ8d/4xro6+lh1ePRuPs6dXTaJtGbd1VuUXXYaex48rwKxkWOIwA5wBsVDbsz9nPJ0c+oU6po1pbzfL45UYd+z4+fZgcPplI90jc7d3JLMtkydElJJckA/BV/Fc8EvcIjjaOzR7f0caRYYHD6OvTl5LqEr499W2DffTz6719ssjI7jq5MFezGujOgdQiYvxcKaoq4v7190suFKIDvLrrVUOnvo93H+7vfz/FNcUs3LuQgqoCViWtYnjgcGZ1m2V4jSlz49v73jZ06m11/pRkXsEL14bx78PvUqWt4sfEHxkeOJypUVO77HmiXlltCfahS6hV1Q/Fl9wo9KRj30VMjZzKU4Ofwtn2fOX5McFjuP7X6zlVeArA8McM9Vcq9TzsPXh04KNAfeL87cxvnCg4AUCdUtfssbemb6VOV79fuFu44QpgjNtAlh74HbV9HiU1Jfxy+hfm9Z5HjbZ+yTc7tZ2hDVuNLQDV2vqlkDLKMvj3oX/T06snc3vObeVvw/iK5YV3yi6+Krnlxi28f+B9NqRuoKymjFjvWJ4d8qzRSX9LdffsziD/QQzyH0RBVQFv7X0LgMyyTOD8HNOfk5aTVVt/IqtWqVl85WK6e3Y3tDM6eDTTfpxGZV0lpbWlLDqwiH+N+1ejx+zt05tgl2AAYr1jjd7b7qzdjSbs7p7dO/zLTIiOEuUexcLxC422jQweycnCk2xK2wRAWY1xQaKXRr7UoB03Ozce3/Q4UD9tqbquukUnryODRjIyaCQAPyX+1ETHvgA7jZow7/oc2FVyYVld/Z2nA2lFzBkcytJjSw2desmFQrSfitoK9mTtMTx+duizDPAbAEB2eTbvH3gfqO8oX9ixN1VuLK4u5tfTvxoel6XPIsqlN3f2G0ct5Xxw4APD8adGTe2y54l6S48tNXTqVUhuFOdJ8bwuYnDAYKNOPdRX1gx3Czc8drBxMPwc7RFtmD9fVF3E+/vfZ+fZnXx+7HPD0CRnW2ejOThNKa09f5HAyeb8PP6jGcUoOnvD471ZewHo79sfVztXThac5FjeMdJL09mdtRsbtQ3DA4cD8MrOV6jR1jB/xPx2vUo4d+Vcvj/1PQVVBdToajice5gH/3iwwYl/a+kUneFn/ZCx3kHu2GpUJFedH8o0LmScUbIG8HPyY2bM+Su3m9I3UautbfaYLrYuRo9rdc2/RghrV1FbwbaMbRzMOWjYpu94N6ZWV0tycTIrElcYtvXy7tWiKUktkVNaRWJOGQPCPBgSGNelcmGAsz8atcqw5N2a5DWG5yQXCtF+ymvLjf4WL6y5dOHPiUWJFFUVNdrG5eTG/dn7DX+HGpWGmvIQwzJ3cX7nazAdyz9GWU1Zlz1P1LswN/rbxEluFAZyx74LK6wqZOfZnYbHE0InGH52sHFg0RWLeHHbiyQUJrD4yGIWH1lseH5E4AieGfIMAc4BzR4n0j3S8LP+rtjwwOH8lrAetcP5q5AZ5RkAeDp48u74d1mwYwE3/X4TAD6OPrw+5nWiPKJYeWYl2zK2MbfnXMOcp6KqIuxt7Ft0x6w1ymvLeXXUq6hVal7f9TqltaUUVxezMmklN/S4oVVtnSo8hVqlJqMsgy+Of2HYfmvPWwFwsNUQG2RPsub8/LZe3r0abevCuV6VdZWklKQ0KPh1ocKqQt7b/57RtljP2Eb3bWzu1dyec3l26LNNti9EZ/POvndYcnSJ0TZ3e3duib2Fm2JvarD/meIzXPfTdUbb1Co1o4JG8fcRfzdZXBeuX9/VcuHcXrfyZborJ7NLyS8vJaMsw/Cc5EIh2o+Xgxfu9u4UV9evVPTZsc94buhzlNSU8FPiT0b7ZpZnGnXWTZEbL6yhYadyBTSGjr234/klPxUUMsoy6OHVo0vlRv15ItRfjL4wN5aVNH4eLrmxa5KOfRdVWlPKoxseNQy5HxU8imuirjHax93OnRiPGE4XnTa6cghwMPcgm9I3XTJJ6I0LGUdPr56cKDiBTtHxyIZHDM9dUIPFMLQKYGjgUH6f9Tt5lXnU6erwd/JHpVJRXF3Mv/b8C38nfx6Je4Qt6Vt4bddrZJRloEJFnF8cL418yehiwuX4v+H/x6TwSQDsy97HDwk/APXVWFvrjd1vGD32c/Tj4biHjeZN9Q6xI7no/D5eDl6NtuXtYLy2dVlt41eGmyp2Msh/ECOCRrQgaiG6DhUqdIoORVFA1bL91So1WkVrshjOr19f/7ff1XLhsfgjHD9bwt4046GnkguFaD8atYZ7+t5jGPr9y+lf+OX0L43ue+G5WlNamxv1q4MA1GnrBxPrl3SzVdsa7VtRVwF0vdyod+FUWYC8YjsKy2vwdLYz2i65sWuSjn0XlFWexQPrHyCxKBGAYQHDeGf8O0bLmJTUlDB35Vzyq/JRoeLVUa8yOXwymWWZPLHpCZJLknlv/3uEuIYwJeLSlTJt1DZ8NPkj/rHzH6xPXX/+IoHWBVVtIIpD/dB+Nzu3Bq+9eDm9t/e9TX5VPu9NeI/cylye2PgEtbpaHh7wMMklyfx25jce2/gYP1z7g2G+1eUYEjDE8POFJ5b6q9qXI68qj4SiBKNtg0KD+L3o/OOCqsbXKL24au3Fw6ea4mzrzHXR1/HowEeNKtteqLGiKH5Ofi1qX4jO4sYeNzIuZBwlNSUcyDnA58c/p6i6iP8e/i91ujoeH/S40f5BzkF8NuUzqrXVpJak8sWJL0guSWZz+mYSChP4deav2GnsGj9YK+xsYv36rpILB4R6sHxXKglZxkNAJRcK0b7m9Z6HWqXmf4f/R1F1EVB/5/3K8CtZnbzasN/F52qmyI0X3kWv0dYS7OFIsEf9touHkF98x72r5EY9VztXo8cqmzL2phQyuZfxcH3JjV2TdOy7mITCBB5Y/wDZFdkAXBVxFa+Nfq1B0l2fst6QFLp7due6mPphVjGeMdzQ4wb+tedfhv2a69hDfbJbOH4hpTWlpJakUl6l4YZFp4josZp8EgzHuZS9WXv5MeFHrgi7golhE/nf4f9Ro6thoN9A7ut/H5V1laxJXkNScRLH8o8ZCr9cjgvX/7RRn/9zaWzZvuYsuWoJfXz68N3J73hz75voFB3Lji+jh2cPw+93eEQgun2eqO0KATiRf6LRto7nHzf87KBxaLbaqVqlxt3enTDXsGbnmklRFNEVBLkEEeQSBMD40PFoVBrDdKNfT//aoGPvYONg+LsYETSCEUEjuObH+lFOmeWZ7M3ee8m5+S2RU1LF6dxyhkV64WDb9N+pNefCuNCJABzPqCbYJdgw5FRyoRDt77Zet3FL7C0kFSdRo6shzDWMU4WnDB17RxtHQt1CjV5jitwY4hpy/oGmnEHh5y8e5FWeX85NhYoQlxCaYs25UX+e6GTrZJQb1Q4Z7EkuaNCxl9zYNUnxvC5k99ndzFs1z9Cpn9drHm+OfbPRK6kX3h0pry03eu7C4TwXP9ccVztXevv0prDYA5VtEUXqXYbn9EOZGlOjreHlnS/jZOvE34b+DcCwDIh+nr+jjSOe9vV3ufTv0dI42jhye+/buTryasO29/a/Z6jiGuLpiG31+UIxm9I3kViYaNRGXmUePyb8aHg8PnR8k1fDe/v0ZqD/QAb4DSDSPVKWIxFdXlVdVaPbLx6x1Nz+F9/JuPA1bbUz6fz8+qZYey4M8bLF1d6Gg6lFXBlxpeE5yYVCdAyNWkOMZwy9vHvhbOvM/478z/DcuJBxhqHxpsyNA/0GGjrFKpWOIP9cw3P7cvYZfu7p3RMXu8bvPFt7btSfJwJGudHG5QRbU44atSG5seuSO/ZdxB8pf/D0lqcNFS6vjryaiWETOZBzwLCPvcbeUGzjwrvn6WXpvLT9Ja4Mv5KM8gyWHV9meK639/niHD8l/sSL214EYLD/YJZOWWp47o3db6AoCnF+cbjZufH1ye04RfyAlvq5WkMChjAqaFST8X985GOSipN4buhzhuqg+qu2+iFjdbo6QwV+o6u/FujB/g+yJnkNOkVHbmUu35/6nlt73opKpSLOdQa7a/eiti1Bp+i4Z9093NP3HsP6pIuPLDbMMXO2debhuIdNGtupwlNoVA0Tex+fPiYZaiyEOT2y4REcbBwYFTSKYJdgFBQO5hzk02OfGvbp69vX8PPq5NV8evRTpkROMazVnF6azufHPzfso1ap6ePdx/D4UrmwsKqQ/Tn7AeO70FXaKn48uRoblzxcPTVA4yOYrD0Xrkj8gf6hMWxNzGNa2C38fuZ3cipyJBcK0c52n93NkmNLuCLsCoJdgsmvzOenxJ/YnbUbqL/re3//+w37mzI3ejh4MC1qmqFQ38b8RcQlqymqKmLJkfNFTm/rdVuT8Vt7btSfJwLc2ftOQ25UqRRS7d7hs6M19PTuJrmxi5OOfRexIW2D0bIVq5JWsSppldE+F67TOTp4NMMCh7HrbP0d9R8SfjAUBNELdQ29ZJK9UFF1Eb+f+Z3l8csN2/QjlmK9YvnX2H81OZfnTPEZPj7yMX28+3Bz7M2G7dOip/G/I/9jT9YeNqRu4FThKSrrKonzi6OXV+MVlC1FhHsEV4Vfxark+v8HS48u5YbuN2CrsWVoeBibN/6F4B5fU1SbRV5lHq/vfr1BG572niwcv9BoyUJTuLh4i97q2asNa50K0VnV6erYlLbJsGb9xTzsPXh2iHFl39PFp/nw4IdNtvnQgIdafJKYWJTI4xsfb7C9oKqAAt7BMRS+TQ7k7sENpzh1lVw4OeRdtibmcSYb/jPpPzy64VEyyjIkFwrRjrSKlm0Z29iWsa3Bc/Yae94Y+wbRHtFG202ZG58a9BQ/H9+FYneWzIpU/rr5r0bPT4+ezrSoaY2+tqvkRv15oqeDp1FuVNmU8ta+hvlKcmPXIx170Si1Ss1/rvgP35z8hrUpazlddJry2nLsNHaEuoYyLmQc83rPM5pbdCnjQ8aTV5HHmeIzFFUXUVunQVXrz9Ojb+TGHjc2eYVPURQWbF+AoijMHznfaLisj6MPS69aylt73+L/tv0fDhoHpkdP56nBTzV5kcCS3NPvHlYnr0ZBIbsimxUJK7gx9kbiwjzQVQcwyvE1eg+IZ0PqBhKLEimrKcPR1pFIt0jGhIzhph43mWztbCG6ijnd5+Dp4El8QTwFVQVU1VXhZOtEhFsEI4JGcHPszUbFmPr59uPGHjdyOPcw2RXZlFSXYKO2wd/Zn34+/ZjdfTaD/AeZNEZVIyX5u1IurPLdAQRxMK2IKX1iWTF9BT8k/CC5UIh2FOoaytTIqRzNO2qoNO/n5MfIoJHc0fuOBnPrTZ0bC8tsKTlzP7Gx+7B3P0pGWQY2ahu6eXRjdvfZXBd9XaOv60q5UX+eCPUja1dMX8GCTUv4JWEtzq55aJVKyY1dnEpRlNZXdxDiMqQVVDDmXxuZ1NOPj+cNaf4FXUxFTR195q+hZ6Abvz86xtzhCCE6wK+HMnnkqwM8ekU3npx86UKi1i6vrJrBr65neJQXX98ryy0J0RV8uyeNZ344zN+ujuW+cdHNv0AAcLa4khGvb2B0jA9f3D3M3OEIM5PieaLDHU6vXwKkb7CHeQOxUE52NsQGuBGfVUpljenWxxZCWK5dSefWr49sfL32rsTHxZ4QT0eOpBej1cm9ByG6gj3J9cVDh0gObJVAd0dCPB3Zn1pInVZn7nCEmUnHXnS4wxlFAPQLadkw/q4oLswDrU7hSMblr4MqhLB8O88UYKtREXfR+vVd1YBQD8prtCTklJo7FCFEB9iTXICDrZo+QXJu2FpDI7yoqNFyLPPyV2cRnZt07EWHO3Lujn2fYEneTdGf3B9ILTRzJEKI9pZXVk1iThkDQj1wtJOlhqC+Yw9wMLXIrHEIIdpfTmkVyfkVDAj1wM5GuiatpR/loB/1ILou+esRHUp37i50kLsDvq725g7HYsWFeQBwQE5qhbB6u8+tXz8ssun167safQ48mFZk1jiEEO1PnwOHRsgw/LYYEiEde1FPOvaiQyXnl1NaVUe/EA9zh2LRIr2dcXe0ZX9qIVLfUgjrtvPMufn1UdKx1+sd5I6NWiUdeyG6gB2nJQdejmhfZ7yd7dibLOeMXZ107EWH0t+B7hcqw/AvRa1W0T/Ug5zSas4WV5k7HCFEO9p1pgAbtYqB4R7mDsViONhq6BnoxsnsUsqq68wdjhCiHe04k4+djZqB4VJjpC1UKhWDIzzJL6/hdG65ucMRZiQde9Gh9p2bMz5ICkQ1K+7cHFMZji+E9Soor+Fkdin9QtxxsrMxdzgWZWCYB4oCh+WuvRBWK7ukijO55QwM88DBVmqMtJUMxxcgHXvRwfanFGKjVslQ/BY4P8dUCugJYa12J8kQ1Kbo797tTZEcKIS10g/DHxHlY+ZIOjdDxz5JOvZdmXTsRYcprarlZHYpvYPcpPJzCwyQO/ZCWL2dZ84VzpOOfQODznXs90nHXgirtf10HgAjYyQHXo7eQW442WnYLXfsuzTp2IsOcyitGEVB1mluIQ8nO6J8nTmSUUxNnc7c4Qgh2sGupAI0apWhEyvOC/ZwJMDNgf2pheh0UhBKCGu040w+jrYa+stIzstio1EzMMyT9MJKzhZXmjscYSbSsRcdRn/XRU5gWy4u1JPqOh3xWSXmDkUIYWJFFTXEZ5XQN9gdF3uZX38xlar+gkdpVR2JuWXmDkcIYWJpBRWkFVQyOMJT1q83gWHn1rPXr7Qiuh75KxIdRl84T6qetpysZy+E9dqdVICiwLAoWbu5KYZ59skyHF8Ia7PjXAd0RLQMwzeFkTH1dQq2JkjHvquSjr3oEDqdwoHUQgLcHAhydzB3OJ3G+Y69nNQKYW308+uHR8pJbVMGyzx7IazWTkPhPMmBptA/pH7017bEPFnPvouSjr3oEIm5ZZRW1TEw3AOVSmXucDqNHv6uONpqOCDLPQlhdXYl5aNWweAIGcXUlF5BbjjYqtkvFzeFsCo6ncKWhDxcHWzoG+xu7nCsgo1GzfAob7JKqmQ9+y5KOvaiQ+w/d7dloBTOaxUbjZq+Ie6k5FdQUF5j7nCEECZSXFnL8bMl9Al2x9XB1tzhWCxbjZp+IR4k5ZWTX1Zt7nCEECZy/GwJeWXVjOnmg41GuiOmMvrc6gLbEvPMHIkwB/lLEh1i97l1NaVwXuvJevZCWJ895+bXy/r1zdMPx98vtUaEsBqbT+UCML67n5kjsS6ju9XPs5eOfdckHXvR7hRFYeeZfJztNPSR4VatFhdaf1IrBfSEsB67kurnluqrGIumDTIU0JP1mYWwFptO5gAwroevmSOxLtG+Lvi52rPjTD51WlkquauRjr1od6kFFWQWVzEk0gtbGW7ValIZXwjrsyupAJUKBkdIx745gyO8UKtg+2mp9CyENSiurGV/ahGxAa74u0lBZVNSqVSMjvGhtKqOIxnF5g5HdDDpZYl2t0Oqnl4WfzcHgj0cOZhWhFYnVU6F6OxKqmo5mlFM7yA33B1lfn1z3B1t6RPsztHMYooras0djhDiMm1LzEOrUxjfQ4bht4dRMTIcv6uSjr1odxevU3r27FnuuecegoODsbe3JzIykueff56KiooGr73jjjtQqVSN/lu/fr3RvklJSUydOhV3d3eio6NZtGhRo/HMmDGDq6++ulXvISIiggEDBjT5/IwZMxpU+3/ppZeM4rWzs8PX15fhw4fzxBNPcPjw4UbbGj9+PB4eHkbbBoR5UFZdx+ncslbFLYSwPPuSC9EpMCzSW/JhC/PhyGgfFOX894kQovPSD8Mff4lh+JIbW3+uqKfv2G+Vjn2XY2PuAIR108+vd3WwoXeQO9nZ2QwbNozs7GweeOABevbsyZ49e/jnP//J7t27Wbt2LWp1w+tNy5Yta7CtT58+hp91Oh0zZ86kvLyc119/nWPHjvHII48QHBzMzJkzDfv9+OOPrFu3jqNHj7bPG27EP/7xD8LCwtBqtRQUFLB//34+/vhj3nvvPZ588kneeuutZtuIC/Xg98NnOZhaRHd/1w6IWgjRXnaem1/f3VUr+bCF+XBUjDcfbT7N9tN5TOkT0GHxCiFMS6tT+ONEDm4ONk0WVJZzxbadK+oFuDsQ4+fC/pQiKmrqcLKT7l5XIf+nRbtKyisnu6SaST390KhVvPbaa6SlpfHNN99www03AHDffffRo0cPnnnmGb744gtuv/32Bu3MnTv3ksdJTEzk0KFDbNiwgQkTJgBw9OhRvv/+e0OyLi0t5ZFHHmH+/PlERkaa+J02berUqQ2u4Obm5jJ79mwWLlyIn58fzzzzzCXbMMyzTyvkhiGh7RSpEKIj7DxTP79+4zf/lXxIy/Lh4HAv7DRqGVoqRCe3N7mA/PIaZsUFN1l3Sc4V67X2XPFCo2N8+DQnmZ1n8pkY62/iaIWlkqH4ol3pix3pl3TatGkTjo6OzJkzx2i/O+64A4BPP/200XYURaGkpASdrvEKn+Xl5QB4e5+fx+/l5WXYDvDCCy/g7e3Nk08+2ab3Ykq+vr6sWLECFxcXXnvtNaM4G9M7yB1bjUoK6AnRyZVV13E0o5jYADd2bPtT8iEty4eOdhriwjw4nVtOVnGVGaIUQpjC6mNZAFx1iZE3cq5Yr7XniheaGFtfv+CPEzntFZ6wQNKxF+1Kv07pmG7186iqq6txcHBoMMfIyckJgD179qAoDQvEubu74+7ujpOTE1dddRV79+41er5Hjx54enry6quvkpSUxO+//87q1asZNWqUod2PPvqI//3vf9jYtG2gilarJS8vr9F/NTU1rW7Px8eHWbNmUVxczLZt2y65r4Othl6BbpzMLqWsuq5N8QshzG9vcgFancKwSC/JhxdoST7Uzxvdflru2gvRGSmKwtpj2TjYqhnbren59ZIbz2vNueKFhkV54WSnYWN8TqO/K2GdZCi+aDc1dTq2J+YR6O5Ad38XAHr27MnJkyc5fPgw/fr1M+y7ceNGAMrKyigsLMTLq34JKH9/fx599FEGDx6Mi4sLBw4c4N1332X06NGsX7+e0aNHA/XJfsmSJcybN4/vvvsOqB/W9Mgjj6DVarn33nu59957GTZsWJvfz9GjR/H1Ne16q/379wfg5MmTXHnllZfcNy7Mk0PpxRxOK2LkuRNcIUTnsiupfi324VHeHJJ8aKS5fDi6mw9vrzvFppO5zBoYYtJjCyHa39GMEjKKKpnSOwBHO02T+8m5orHWnCvq2dtoGB3jw9rj2cRnldIz0M2kMQnLJB170W72phRQXqPl2v5Bhquujz76KD///DM33ngj7733HrGxsezdu5dHHnkEW1tbamtrqaioMCTrf/7zn0Ztzpw5kzlz5jB48GAeffRR9u/fb3huxowZpKenc+LECby9vYmOjgbgrbfeIicnh9dee438/Hwee+wxNm3ahK+vL88//3yDoV5NiY6O5qOPPmr0ufnz57N9+/ZW/47c3OoTbUlJSbP7xoV58Ol2OCAdeyE6Lf3yn8MivbCXfGikuXzYP8QDHxc7Np7MoVara3J+rhDCMq0+dhaAq/pces63nCsaa8254oWu6OnH2uPZbIjPkY59FyEde9Fu9MPwx3U/f+VywoQJfP755zzxxBNcddVVANjY2PDss8+ydu1a9uzZY0hgTenbty/Tp0/n+++/JycnBz+/8+ugurq6MnToUMPjlJQUXnrpJT777DPc3Ny46qqrKCoqYsWKFezevZsbb7yRsLCwFl2ddXFxYdKkSY0+19RyKc3RJ+nm3jNAXGh99dgDqYVtOpYQwrzKqus4klFMz0A3PJ3tJB9epLl8qFGruCLWn2/2prE7qcAwNF8IYfkUReGXQ5nYadTNFnOT3GisNeeKF5rQo/49b4jP4aEJMW06tuhc5HK3aDebT+aiUasY1c345Gvu3LlkZmayf/9+/vzzT7Kysnj11VdJSUkhICCgRYkrIiICgLy8S8+1fOihh5g4cSKzZ88mMzOTtWvX8vrrrzN06FAefvhhRo4cyZIlS9r8Hi/XwYMHgfp5X80J9XLE29mOg2lFMl9KiE5oT1L9/PoRUecLN0k+PK8l+XBSr/oOwbrj2R0RkhDCRPanFpJWUMkVPf1wd7Rtdn/Jjee15lzxQn5uDvQNdmd/aiEF5a2f3y86H7ljL9pFVnEV8VmlDI3wws2hYQK3tbUlLi7O8PjgwYPk5OTwl7/8pUXtJyQkABhdgb3Yt99+y+bNmzl27BgA6enpAAQHBxv2CQkJIS0trUXHNLX8/Hx++ukn3N3dDfO/LkWlUhEX5sH6EzmkF1YS6uXUAVEKIUxlx5n6Yfgjor2Ntks+bHk+HB3jg4OtmnXHs5l/ba8GxbWEEJbpxwMZAMyIC25mz/MkN7b+XPFiE2P9OJJRzOZTOcyMk9ok1k7u2It2sf5E/d2U8bHNFxCpqanhySefxM7Ojqeeesqwvby8nOrq6gb7b9++nd9++43hw4fj49P4UMzi4mIef/xxXn75ZcLCwgAICgoC4MiRI4b9jh49atjekfLz85k9ezalpaW88MILhkqvzRkQ6gHUX/kWQnQuO07no1bB0EivJveRfHjpfOhop2FMN18yiio5cba0A6MUQrRVTZ2O3w+fxd3RlvE92lZYTnJjy88VL3RFz/qLGmuPySinrkDu2It2sfpo/TqlU3obr1NaVlbGsGHDmDVrFhEREeTl5fH5558THx/Pxx9/TK9evQz7JiQkMHXqVK677jq6deuGk5MTBw4c4NNPP8XJyYkPP/ywyeM/99xzBAYG8uijjxq2hYSEMH78eB577DEyMzPZt28fx44du2Q7prBy5UqOHj2KTqejsLCQ/fv38+OPP1JWVsbTTz/N008/3eK24sLq59nvSynkugEtv+othDCv4opajmYW0zfY3TAMVfJh2/Lh5F7+rDuezdrjWfQKkoJQQli6LadyKayo5eahYdjbNF0NX09y4+WdK16ob7A7wR6ObDyZQ0VNHU520vWzZvJ/V5hcYXkNO87k08PflShfF6Pn7Ozs6Nu3L8uWLePs2bO4uLgwatQoFi9ezMiRI432DQgI4IorrmDjxo18+eWXVFVVERgYyNy5c3n++ecNlUwvtmPHDj755BN27NiBRmP8BbJ8+XIeeOAB/v73v+Pj48Mnn3zCuHHjTPsLuMgLL7wA1A8pc3NzIyoqirvuuos777zTaBmXlogL88BGrWL3uSWzhBCdw66kfBQFo/n1kg/blg8n9fRHo1ax+mgWj0/q3p7hCiFM4Pt99cPbZ7ZwGL7kxss7V7yQSqXi6j4BfLw1iY3xuVzTL9BUIQsLpFKkCpcwsW/3pvHM94d59IpuPDlZTrpMbda/t7E/tYgDL07G09nO3OEIIVpgwa/HWLotmaV3DjFUKhZtd+vHO9mWmM+Gp8Y1uIAshLAcuaXVjHj9D0K9nNjw1Dipi2EG+1IKmf2f7VzTN5APbx1o7nBEO5I59sLk9MPwr+4T0Myeoi2GnbvjtztZ7toL0VnsOJ2PRq1iSETT8+tFy03pU3/XadW57xshhGX6fl86dTqFG4eESqfeTOJCPQh0d2BDfA6VNVpzhyPakXTshUmVVtWyNSGPCG8nYgNczR2OVRp2rvDWrjPSsReiM8grqyY+q5R+Ie642MsMOFO4qrc/KtX5C8lCCMujKArf7EnFRq1i9kCpyG4uarWKKX0CqKzVsulkjrnDEe1IOvbCpDbE51Cj1TGlT6BcmW0ngyO80KhV7ErKN3coQogW2HIqF4Bx3dtWDVo05OfqwJBwL45kFJNWUGHucIQQjdhxJp/k/Aom9/LH19Xe3OF0adPOza3/+WCmmSMR7Uk69sKkZBh++3Oxt6FPkBvHz5ZQXFlr7nCEEM3YLB37djHl3PeM3LUXwjJ9vbt+7febhoaZORIxMMyTcG8n/ojPprC8xtzhiHYiHXthMpU1WjadzCXI3YF+Ie7mDseqDYvyRlFgr8yzF8KiaXUKW07l4ulkS78QD3OHY1X0HftVR8+aORIhxMUKy2tYfTSLYA9HxsQ0vo686DgqVf10iFqtwq+H5a69tZKOvTCZzadyqKzVclWfABmG385GRNcX0PszIc/MkQghLuVIRjGFFbWM7e6LRi150ZSCPBwZEOrB/tQisoqrzB2OEOICKw5kUKPVceOQUNSS+yyCfrnBH84tPyisj3TshcmcH4Yva2S2t+GR3tjZqA1DfIUQlklfqEiG4bcP/bSvNcdkOL4QlkJRFL7enYpaBXMGS9E8SxHq5cTwKC8OpReTkF1q7nBEO5COvTCJ6jotf5zIwcfFnkHhnuYOx+o52mkYFulFUl45Kfnl5g5HCNGETSfrL76NlY59u9BfSF55RIbjC2Ep9qcWkpBTxoQefgS6O5o7HHGB6weFAvDNnjQzRyLag8nX3SmsKuTjIx+zKW0TWeVZONg40Mu7F3N7zmVc6LhWtVWrq+Xr+K/59fSvJJckAxDpHsm1UddyY+yN2Kptjfbv+1nfS7a3aOKiVscgWmZ7Yj6l1XVMHxBkEcNNN6ZuZHn8co7nH6eqrooA5wDGh47nnr734OHg0eJ2EgoTWHxkMXuz9lJYXYinvSeDAwZzb997ifGMMdr33wf/zX8O/afJtnp59+Kbad+09S01MK67L38m5LHlVC63jXA2WbuiY0nOtF65pdUcSi+iX4g7Pi6WUxHamvJjmLcTvQLd2JNcQF5ZtUX9noXoSJb2XeLaE3YDfT+T7xJLck3fQBb8eozv9qXz16t64GCrMXdIFsMavhtN2rHPLMvkjtV3cLb8/JXzmpoadp7dyc6zO3lowEPc3//+FrVVq63lwT8eZOfZnUbbj+cf53j+cbZmbOWDKz5okFyEeeiLF1nCMPwPD37IR4c+MtqWWprK58c/54/UP/h0yqcEODdftX9rxlYe2/AYNbrz1UNzK3NZlbSKDakbeH/i+4wMGmny+FtqfA8/Xv39BJtP5XLbiAizxSHaTnKmdVt/IhtFgSt7+Zs7FANrzI9T+wZw/GwJa49lc8swqb4tuh75LhEt5WinYc6gUJZsS+LXQ5nMGRxq7pAsgrV8N5q0Y//37X83JJV+Pv34S9+/kFScxAcHPkCn6Pj3wX8zPHA4A/wGNNvWkqNLDEnFy8GLpwY/hQoVb+19i4KqArZlbuOzY59xd9+7G7x2dPBo7ul7T4Pt0R7Rl/cGRaPqtDrWHc/G3dGWYVFeZo1lX/Y+/nvovwCoVWoeiXuESPdIlhxdwuHcw2SUZTB/+3z+O/m/l2ynuLqY5/983vCHOT16OleGX8nalLX8cvoXqrXV/O3Pv/HbzN9wtXNt8PqF4xbi42hcBdbZ1rR31aN9nQn2cGT76Xyq67TY28hV185GcqZ1W3tu3veVvS1j+U9rzY9T+gTy1tpTrDp6Vjr2okuypO+ScPW1LP4ziVkDg7n53DJ38l1iWeYOD2PJtiSW7UyRjj3W9d1oso59QmECu87uAkCFioXjFxqubKSXpvNDwg8oKCw7vqzZxKLVaVkev9zw+OkhTzMtalp92yoVf/vzbwB8eeJL7ux9Jxq1cYfGy8GLgf4DTfXWRDN2JxVQWFHL9YNCsNWYt2zDlye+REEBYGbMTMMXT2/v3lz5/ZUoKGzP3E5iYWKD4TAX+v3M7xRWFwIQ4RbBq6NeRaVSMSZkDIdyD5FSkkJBVQG/n/mdm2JvavD63j69CXYJbod3eJ5KpWJcD1+W70pl15kCmcPbyUjOtG6lVbVsS8wn0seZbn4u5g4HsN78GOPnQjc/F3aczqeoogYPJzuTtS2EpbO075KtB1zRVkbwyMgJhHk7meptChOK8nVhTDcf/kzI41BaEf1DPcwdkllZ03ejyXphu7N2G34OcgkyGq5wYSLZk7Wn2bYSixIpqDq/PvdAv/MnnHF+cYaf8yrzOFN8psHrN6VtYuRXIxm4bCBXfX8VL257keTi5Ba+E9FaqwzV8M1/V+rCz+GFn5UA5wACnQMb3a+5dvr79jcs36dWqenv27/Zdu5YfQdxy+IYsXwEt628je9OfYdO0bXuzbSAfoiv/v+B6DwkZ1q3TSdzqdHquLK3v8Us/2nN+fHqPgHU6RTWn8i5rHaE6Gws6bvkj5SNJDs/iVvs/3HPxpnyXWLB5g4PB2DZzhQzR2J+1vTdaLKOfVrp+eqK3o7eRs9dOKygsLqQ0ppLL7GQXmq8vuKFr794iMKFx9UrqSmhtKaUWl0tmeWZ/JT4Ezf8dgMHcw42+z5E6+h0CmuOZeFib8Pobj7Nv6AdFVcXU1xdbHh88WflwseNfW4udOHzbWknqzyLOl0dZbVlHMw9yMs7XuapTU+hKErzb6QVRkb74OZgw9pjWdRpTX/hQLQfyZnWTb/82pW9zH/BE6w/P+qnO6w/nt3mNoTojCzpu6S8rhSVpgpFVSffJRbuilg/gtwd+OVQJrml1eYOx2ys7buxVUPx92fvb7At0DmQQJdAKusqDdsuLqhx8eOK2opG5xYYnq+raPL1Ddq6YN8ItwiujLiS7p7dcbV15VDeIZYeXUplXSWVdZXM3z6fn2f8fIl3KFprf2ohOaXVTO8fZPY53hd+BqHhZ8VGbdPkvpdqy1bT9Oe5ovb8589eY8+ksEmMDB5JsHMwJTUlfBX/Fftz6v9u1qeuZ03KGqZETGnhO2qenY2ayb0C+GF/OruTCxgZbd6LK8KY5MyuqbpOy6aTufi52hNnIUMcrT0/9g5yI9DdgS0JuVTVaqXSs7AqneG7ZELoJJZsqMZG5cTdk9R8fvxT+S6xYDYaNfNGRvD6qniW7UzhycndzR2SWVjbd2OrOvbzVs9rsO2B/g/w4IAHcbQ5v05lra7WaJ8abY3RY0fbS69p6WRjPCenVleLncau8bYuOO6vM381em5k8Eh8HX1ZsGMBAGeKz5BWkkaomxSKMBX9EPApFjAM/8LPAjT8HF74+OJ9L9VWrfaiz/MFlS4v3O+uvnc1aGdi2ESu++k60svqr4JvTtts0o491FeE/mF/Or8fPisdewsjObNr2n46n7LqOq4bEITaApb/BOvPjyqVikk9/Vm2M4UdZ/KZ0MOvTe0IYYk6w3fJt3vTKCs4zD1jInk4rhcBzn7yXWLhbhoaxvt/JLBsRzIPjIvG0a7rXRC1tu9Gkw3FD3EJMfycV5Fn9Fxe5fnHHvYeuNm5Xbot1xCjx7mVuY22BRDqeukkceGcBoD8qvxL7i9aTlEUVh/NwsFWzfge5i/c5m7vbvTZuvBzA8afnYs/Yxe78PN8cTv5lec/Q819/uw0dvT07tnoa01ldDcfPJxs+e3wWapqtSZvX7QPyZnWS18N/yoLqYYPXSM/TjpXc0SG44uuxFK+S77enQrAjUPqK+HLd4nlc3e05aahYRRW1PLD/vTmX2CFrO27sVUd+yPzjjT49+CABwEYGjjUsN/Z8rNklZ8v5qUfTgAwJGBIs8eJ8YjBy+H8smkHcg402pa3gzfR7vVLaCQUJhgNbdA7mHvQ6PHFcx5E2x1IKyKjqJIrYv1xsjPpyoltNjTg/OfwwjldmWWZRuu7Xrhfo+1c8Hk+nHvYML9Fp+iMPo8Xfp4P5x5u0E61tprj+ccNj32dTH8BxN5Gw3X9gyiurGX9CTmhtSSSM7serU5h3fFsXB1sGB7l3fwLOpC158fhUV4422lYfyLb5PVMhDAnS/8uOZyRw/7UIoZGeBFzbhUQ+S7pHO4cFYFGreKTrUnodF0zb1rTd6PJemPdPbszNGAou7N2o6Dw1KanDOto/nL6F6B+GY65PecaXrMnaw9/WfMXAIKcg1hz/RoANGoNN8XexL8P/huAN/e8afjlvLXnLcPrb+l5i2GpjXUp6/g6/muuibqGwf6DcbRxNMwX1evp1bPZqy2i5X4/XP9hv6ZfYDN7dpxbet7C+tT1APyY+CMhriFEukfyyZFPDPsMDxxON89uANy5+k72Zu8F4JVRrzAjZgYA06Km8Z9D/6G4upjkkmT+b9v/cWX4laxJXmMoeuFp78m06GmGdm9deStDA4YyOXwyEe4RFFUX8dWJr8goyzDsMzl8cru87+sHhfLZjhS+35fOtH5B7XIMYVqSM63TrqR88spqmBUXjJ2NeZf/vJi150d7Gw3jeviy8kgWRzNK6BviflntCdEZWMJ3ySeHv8Derx/9e0xge4Yi3yWdSIinE1P7BvLroUzWn8g2FCLtSqzpu9Gkt1kXjFzAHavvILsim8N5h3l84+NGz9/f//4Wr5V8V5+72Je1j11ZuyioKuD5rc8bPT88cDh39rnTaFthdSFfnPiCL0580aA9T3tPXh39auvekGiSTqfw++GzONlpLGou45CAIdzT9x4WH1mMTtHx3v73jJ4PdA5kwcgFzbbjbu/Oa6Nf4/GNj1Orq+WX078YviAB7NR2vDbmtQbD2nZn7W5yGYs53ecwPnR8699UC/QJdqOHvytbTuWSVVxFgLtDuxxHmJbkTOuz8kj9Bc+pfS3ngqdeV8iPk3r6s/JIFutOZEvHXnQZ5vwuqdPqqFFKsfPextep2/g61bg9+S6xfPeMieTXQ5l8/GdSl+zYW9N3o0k79iGuIXwz7Rs+PvIxm9M3k1WehYONA728enFrz1uZEDahxW3Zaez4z6T/8FX8V/x25jeSS5KB+sqb06KmcXPPm40qDM7qNgtHG0e2ZWwjtTSVgqoCVKgIcQ1hTPAYbu99uwwDMqH9qYVklVRxbf8giyu28ejAR+nt05uvTnzF8YLjVNVVEeAcwPjQ8dzd926jYWaXMjZkLF9d8xUfH/mYvdl7KaouwsPegyH+Q7i739109zSuIPr+hPfZnL6ZQ7mHyK3MpbymHDd7N3p792Z299lcEXZFe7xdoL5w1JzBIbz6+wl+2J/OQxNi2u1YwnQkZ1oXrU5h9dFsXO1tGNPdMn931p4fJ/TwQ62qn2ffVas8i67HnN8l7trRVGWnEhqcio19gXyXdEL9QjwYGunF7qQCDqQWEhfmae6QOpy1fDeqFJmIJtrgpV+O8en2ZD6aO8giKuILyC+rZsTrG/B1tWfz0+Ox0VjWMGAhrN2O0/ncvHgns+KCefvGAeYOp8u64b872J1UwLbnJhLscekqxkKIy3PT/3aw80wBqx8fQ2zApYvzCcu1IT6bv3y6l0k9/fl43mBzhyPaSM78RavpdAorj5zF2U5jEdXwRT1vF3um9Q8ko6iSP+JzzB2OEF2OJQ/D70om96yvjv+HFBMVol2dyS1j55kC4sI8pFPfyU3o4UevQDfWn8jmeGaJucMRbSQde9Fqe5ILyCmtZnIvfxxsLWsYflc3b0QEAJ/vSDZrHEJ0NVqdwqqjWRY9DL+r0C97t06WvROiXX2zp74g2M3nlrgTnZdKpeKRifXTOD/clGjmaERbScdetNovhzIBuEaqr1uc/qEeDAj1YFtiPgnZpeYOR4guY3dSAXll1Uzq5Y+9jVzwNKdIH2eifZ3ZeSaf0qpac4cjhFWqrtPy3b50XOxtmNZfRilZg6t6B9DNz4WVR86SmFNm7nBEG0jHXrRKVa2WXw9l4ulky7juMgzfEs0bGQ7A5ztSzByJEF2HDMO3LJN6+VOrVdhyKs/coQhhldYdz6agvIYZcUE42Zm0FrcwE7VaxcMTY1AU+PdGuWvfGUnHXrTKHydyKKmqY3r/IItbo1nUm9o3EB8XO37Yn06J3K0Sot3VanWsPHK2fhh+NxmGbwmuNAzHzzJzJEJYp692169rd/NQGYZvTa7pG0iEtxM/H8okOa/c3OGIVpKemWiV7/fVz6eaPSjEzJGIptjbaLh5aBgVNVq+PTf/TQjRfracyiW/vIZr+gVK3RELMSDUE29nOzbE51Cr1Zk7HCGsSnJeOdsS8+kf4k7vIHdzhyNMyEaj5uGJ3dDqFN5ed8rc4YhWko69aLGckiq2JOTR3d+FvsGSyC3ZbcPDsdWo+HR7MlqdrGgpRHv6YX86ALMGygVPS6FRq5gY60dJVR07z+SbOxwhrMqn25MBuHVYuHkDEe1iZlww3fxc+OVQJkczis0djmgF6diLFvt+fzpancLsgSGoVCpzhyMuwc/NgWv7B5FeWMnaYzIUVYj2UlRRw/rjOYR6OTIkwtPc4YgLXNu/vsDrTwcyzRyJENajuKKWb/em4eNix/QBUkTZGmnUKp6+qgcAb645aeZoRGtIx160iFan8OXOVOw0aq6XYfidwl2jIwH4eGuSmSMRwnr9dvgsNVods+LkgqelGRntjY+LPWuOZVFVqzV3OEJYha/2pFJRo+W24REy9ciKTe7lT1yYB5tP5bLjtIx66iykYy9a5I8T2WQUVTKtfyDeLvbmDke0QO8gd0ZEebMvpZADqYXmDkcIq6MoCt/ura9jMWtgsJmjERez0ai5tn8gZdV1rD8ha9oLcblqtTo+3ZaMnY2aW4dL0TxrplKpeHZKLAD/WHlcpnV2EtKxFy2iXzpt3ogI8wYiWuXuMfV37T+Ru/ZCmNyBtCIOpxczppsP4d7O5g5HNGJmXP0Fl58OZJg5EiE6vxX708kqqWJWXDA+cpPH6g2P8uaq3v4czSjhGynG3ClIx140KyG7lK2JefQPcad/qIe5wxGtMKGHH1E+zqw6mkVGUaW5wxHCqny6LRmAO0ZGmDUO0bS+we5E+Tiz6WQuBeU15g5HiE6ruk7L+38kYqNW8dCEGHOHIzrI/13TC3sbNf9aE0+h5FCLJx170ayPNp8B4M5RkWaORLSWWq3iztGRaHUKn52rYiuEuHxZxVWsPHKWcG8nJvTwM3c4ogkqlYrZg0Ko0ymG5VqFEK337Z40MooqmTM4lFAvJ3OHIzpIqJcTD46PoaiiloXrpJCepZOOvbiktIIKfjqYQZiXE9P6BZo7HNEGswcG4+5oy1e7UimrrjN3OEJYhf9sSqROp/CXUZGo1VI0z5LNGRyCjVrF8l2p6GSeqBCtVlxRyzvrE7CzUfPIRLlb39XcNy6KUC9HvtyVKsvfWTjp2JuYTqfjnXfeITY2Fnt7e0JDQ3n66aepqKholzbWrl3Lfffdx6BBg7C3t0elUnHw4MFLtn/8+HFuueUWAgMDsbe3JyQkhJkzZ5Kd3bC40H+3nEarU7h/XDQ2Gvm4dEZOdjbcOiyM0uo6vm1kjlRmZia33347vr6+ODo6MmTIEH744YcWt3/y5En++te/Mn78eNzc3FCpVLz77rtN7v/6669z/fXXExERgUqlYsCAAW14V6KzseTcuGHDBmbMmEFkZCTOzs54eHgwcOBA3n//faqrqxvsf7a4kq92pxHg5sCNQ0JbHL8wDz9XB67qE0ByfgXbm6juLHlQmNrJkyeZMWMGnp6euLi4MG7cODZt2tQubSQnJ6NSqRr9N3r06Ab719TU8Morr9CjRw/s7e3x9fVl7ty5pKamNhrH2+tOUlBewwPjognycGzVexCdn4OthvnTeqMo8PyPR6jT6oyev9z82do2Wpo/L/V3of+3bdu2VsVp6WzMHYC1eeKJJ3j//feZOXMmTz31FCdOnODdd9/l4MGDrF27tkXLIbWmjeXLl/PVV1/Rp08fevTowZEjRy7Z9po1a5gxYwa9e/fmiSeewMfHh+zsbHbs2EFJSQn+/v6GfbOKq/h2bzr+bvbMHiQVnzuz20dE8L8tZ1i6PYl5IyPQnLvDWFBQwOjRo8nJyeHJJ58kJCSE5cuXc/311/P5559z2223Ndv2jh07ePvtt4mJiSEuLo4tW7Zccv/nn38eLy8vBg8eTH6+LKHSVVhybjxx4gQ6nY4777yTwMBAqqur2bJlC4899hirVq1i1apVRvu//0ciNVodD02IluWeOolbh4Xx++GzfLEzhdHdfIyekzwoTO306dOMHDkSGxsbnnnmGdzd3Vm8eDGTJ09m7dq1TJgwoV3amDlzJrNmzTLa5udnPFVIURSmT5/OmjVrmD17No8//jjp6eksWrSITZs2sXv3boKCzq9PfyC1kGU7Uwj2cOSB8dFt/I2Izm5SL3+m9A5g9bEsPt6axP3j6j8LpsifrW2jpfnT19eXZcuWNdheV1fHvffei4eHB0OHDm3lb8LCKcJkjh49qqhUKmXWrFlG299//30FUL755huTt5Genq5UVVUpiqIo8+fPVwDlwIEDjbadnZ2teHl5Kbfddpui1WqbjeW5Hw4p4c/+pizdeqbZfYXle/zrA0r4s78pvx3KNGx75plnFED55ZdfDNvq6uqUIUOGKD4+Pkp5eXmz7ebn5ytFRUWKoijKxo0bFUB55513mtz/9OnThp/Dw8OV/v37t/7NiE7F0nNjUx544AEFUPbt22fYdjitSIl47jdlzD83KFW1da1qT5iPTqdTJry5UYn62+9KemGF0XOSB4Wp3XDDDYparTbKOaWlpUpYWJjSq1cvk7eRlJSkAMr8+fObbXfFihUKoDzwwANG23fu3Kmo1WrlzjvvNGwrr65Vxr+5UQl/9jdlQ3x2i+IW1iu7pFLp99IapfsLK5XTOaWKopgmf7a2jcvNnz/++KMCKE8++WSrXtcZyNhqE/r6669RFIXHH3/caPs999yDk5MTX375pcnbCA4Oxt6+ZUuOfPTRR5SUlLBw4ULUajXl5eXU1TU+5/p0bhnf7k0n1MuRW4aFt6h9YdnuHRsFwPt/JBjmmS5fvpzo6GiuvfZaw34ajYZHHnmEvLw81qxZ02y7Xl5euLu7tziOqKioVkYuOjtLz41NiYysLxhaWFgIgE6n8OLPR1EUmH9tL+xt5G59Z6FSnS8k+vGfZ4yekzwoTKm8vJyff/6Z8ePHGw0RdnFx4e677+b48eMcOHCg3dqoqqq65BQn/VD+22+/3Wj7sGHDiI2N5ZtvvqGyshJFUfj7z8dIyivnlmFhUiRU4OfqwIvTelFdp+PZHw6j0ykmyZ+tbeNy8+fSpUsB+Mtf/nJZ7Vgi6dib0J49e1Cr1Q2GdTg4ODBgwAD27NnTIW00ZeXKlcTGxrJjxw5iY2NxcXHBwcGBiRMnNviCeGvNSbQ6hacm98DORj4m1qBnoBtT+wZwMruU34+cJSsri/T0dIYPH95gX/22y/m8CaFn6blRr6ysjLy8PJKSkvjyyy/55z//iY+PD0OGDAHgu31pHEwr4opYP67o6d9Ma8LSzBkUgo+LHV/vTjMs2yR5UJjakSNHqK6uZsSIEQ2ea+lnqq1tLFy4EEdHR5ydnQkLC+Pll1+mtrbWaB993RAnp4aV7Z2cnKioqODYsWP8b8sZvt+XTg9/V16Y2vOS8YquY/bAYMZ192VPciEf/L73svNnR+fg7OxsVq5cybBhw+jdu7fJ2rUU0mMzoYyMDHx8fBq9SxQcHMzZs2fRarXt3kZTTp48SWZmJrNnz2bSpEmsWLGC1157jX379jFmzBhOnDgBwPbEPFYdzaJnoBvT+wc106roTB6f1B2VCt5df4rUtHSg/nN1Mf229PT0Do1PWCdLz416Dz/8ML6+vkRFRTF37lyio6NZtWoVbm5uZBZV8urvJ7C3UfP3a3td1nGEeTjYarhzVCSVtVo+25EM1H+uQPKgMB1TfKZa24ZarWb8+PG88sor/PzzzyxevJiYmBjmz5/PzJkzUZTzq0H07FnfSb+4CF9OTg7Hjx8H4Ndth3ljdTzeznZ8PG8wzvZSkkvUU6lUvDarL852Gt79ZSfQsZ/1y7Vs2TLq6uqs8m49SMfepCoqKpoc+ung4ABAZWVlu7fRlNLSUgoKCnj66adZtGgRM2fO5JlnnmHFihWUl5ezYMECaup0/N/PRwF4+bresoyTlenu78q1/YI4nVvO7/uTARr9vOk/a62pWC5EUyw9N+o988wzrFu3ji+//NIwTLWsrAxFUXj2h8OUVtXx3NWxhHs7X9ZxhPnMHR6Oi70Nn25PpqSq1pDjJA8KUzHFZ6q1bYSFhbFx40Yef/xxpk+fzt13382GDRu4+eab+f333/n1118N+86dOxcfHx9efPFFlixZQnJyMtu2bWPGjBmGu/sfb4zHVq3mf7cPkjXrRQPBHo48N7Unlec+g7Z2dg32aa/P+uVaunQpTk5O3HTTTSZr05JIx96EHBwcGl0aCernPAE4Ol56mRBTtHGptgHuvPNOo+1XXHGF4Uth8Z9nOJNbzvWDQhgS4dWm4wjL9vRVPbC3UfP1/rMAjX7eLvezJsSFLD036vXq1YtJkyZxyy238NlnnzF16lSuvPJK/vnNBv5MyGN4lBfzRkRc1jGEebk72nLHyAiKKmr57+bThu9FyYOiNbRaLVlZWUb/iovr1/c2xWfKVJ/LF154AYDVq1cbtnl7e7NmzRpCQ0O56667iIyMZPTo0Xh7e3Pr7fXnh7UaB/51fT8Ghct5oGjcrUPDiIusr7uw53ROg+c7+rPeEjt37uT48eNcf/31uLm5maRNSyMdexMKCQkhLy+v0Q9nRkYGAQEBaDSXLrZkijaaEhpav95yYGBgg+cCAwMpKCzkvfUJuDva8rerY9t0DGH5Qr2ceGB8NOW2HsD5YVAX0m8LCQnpyNCElbL03NiUuXPnUltby1uLFuNsp+HN6/vLKCYrcO+4KLyc7fhkaxJ2bvVL30keFK2RlpZGYGCg0b/HHnsMOP95uZzPlCnaAIiIiAAgLy/PaPvAgQM5evQo8fHxbN68maSkJL5b8RNrDyQCcMfVI5gRJ8sci6ap1Sr+eft4ALYfPsXRjGKj5zv6s94S+qJ5d911l0nas0TSsTehwYMHo9Pp2L17t9H2qqoqDh48yODBgzukjaboi06lpaU1eC41LQ2Nkwc1Wh2vzuiDt8vlVZMWlu3+cdF0jwhF4+LFxi3bGjy/c2f9vKnL+bwJoWfpubEpZeX1w/+qK0p5cVovGZJqJdwcbHlkYgxVtTo+2V9EUFCQIeddSPKgaEpAQADr1q0z+vfMM88A0LdvX+zs7NixY0eD17X0M2WKNgASEhIA8PdvvNhnjx49GDt2LOHh4Tzx1V6y4vfh5hfC63de1WzbQvTrHom3XwBVGSd5/JuDVNWer3PT0s9pYGBgh+TgyspKvvnmG2JiYhg7duxlt2eppGNvQjfddBMqlYp3333XaPvixYupqKjg1ltvNdqemppKfHy8UcXS1rbRGrfddhsAH374odH2FStWcDYzE9uIQcyKC+ZaKZhn9RxsNbx94wBceo0jMy2ZT7/63vCcVqvlgw8+wMvLiylTphi219bWEh8fT2pqqjlCFp2YpefG7OzsRrc/9MJrAPQfOJgbh4S2uX1heeYODyc2wJVfDmUy6qrrOH36tNE8ZMmD4lIcHByYNGmS0b9eveqLarq4uHDttdeyadMmDh06ZHhNWVkZH3/8MbGxsQwaNMiwvaKigvj4eM6ePWvY1to28vPzG8So1Wp58cUXAZg2bdol38+76xNY/tHb6CqKeePlF9FopHsgWuaO226lrugsh7f/wUu/HANanz9vvvnmFufgtvrhhx8oLi622qJ5eirlwlKZ4rI98sgjhsJ0U6dO5cSJE7z//vuMHTuW9evXo1KdH8Y5fvx4wxAo/XCp1rZx+PBhfvnlFwA2bNjAxo0beeihhwgICDC0deHaurfccgtfffUVc+bMYeLEiSQmJvLe+x+g2Lsw9umP+e25a3Gyk+qnXcU/f9rDC/OmQXUpz/z1KSLCQvnqq6/YtGkTS5cu5Y477jDsm5ycTGRkJOPGjTOqpltcXMwHH3wAQFJSEkuWLGHq1KmGZXqmT59Ov379DPsvW7aMlJQUoH5pHgcHBx566CEAwsPDDReghHWx5NwYHR1N7969GTJkCEFBQeTm5vL19z9yaN9uXCL6cmr/DgI9pWCetTmYVsSsf2/Dy6aanM+fpLAgnyeffJLg4GDJg+KyJCYmMnToUGxtbXniiSdwc3Nj8eLFHD16lFWrVjFp0iTDvps2bWLChAnMmzePTz/9tE1tzJo1i7KyMoYPH05oaCg5OTl8++23HD58mFtvvZUvvvjCKL5rrrmGqKgoevXqxcHUQj7/5geqkvZz062389UXn7X770dYj/z8fAYOHERGdg4ug2Zw47h+nNqxplX5Mz8/n0GDBpGf33wOhrblz4kTJ7JlyxZSU1MJCrLiG5iKMKm6ujrlrbfeUrp3767Y2dkpwcHBylNPPaWUlZU12HfcuHEKoCQlJbW5jaVLlypAk/8ubru2tlZ54403lO7duyu2traKi4eX4tx7gtLvr18q6YUVpvxViE5Ap9MpdyxarTj3Gq/Yu7gr9vb2yqBBg5Rvv/22wb5JSUkKoIwbN67R7U39W7p0qdH++s99Y/8ubltYD0vOjW+99ZYyduxYxc/PT7GxsVFcXV0V19CeiufEe5Q1h9JM/asQFuSNVSeU8Gd/U2a/9atyyy23Kt7e3pIHhUkcP35cmT59uuLu7q44OTkpo0ePVjZs2NBgv40bNyqAMm/evDa38fHHHyvjxo1T/P39FVtbW8XV1VUZMWKEsnjxYkWn0zXYf8GCBUrPnj0VB0cnRWXroDiE9FRefec/je4rRHPS09OV6bNvUDSObopKY6v07jegVflT38attzafgxWl9fkzKSlJUalUytSpUy/3rVo8uWPfRSmKwnt/JPDu+gR8XOz55r7hRPu6mDssYQZVtVru/mwvWxPzGNPNh//dNhhHO9MWIROis1AUhSe+OchPBzO5c1QE86/tbe6QRDuq0+q49eNd7Eoq4I6REcy/tpfRyA8hrFVKfjmz/7OdvLIa/n3rQKb2bVhYWYjW+OVQJo9+dYBwbyd+eXg07o625g6py5FJNF1QTZ2Ov353mHfXJ+Dnas9X9wyTTn0X5mCrYfHtgxkV482fCXnc+L8d5JRUmTssIcxi2c4UfjqYSWyAK89OkdVBrJ2NRs2iWwYS4e3Ep9uTeX1VPHK/Q1i7vLJqbl+ym7yyGp6dEiudemES0/sHccfICFLyK3jgi33U1OnMHVKXIx37Lqa4opZ5S3bzw/50YgNc+emhUXTzdzV3WMLMHO00fDJvCNf0C+RwejHXfbitwdIlQli7PckFvPzrcdwcbPho7iAcbGXkSlfg62rPl/cMJ9jDkf9tOcOjXx+kskbb/AuF6IRKq2r5y6d7SMmv4I6REdw/LsrcIQkr8sI1PRnTzYftp/P524ojcqG0g8lQ/C4kraCCO5bu5nRuOWO7+/LhLXG4OsgwGXGeTqfwzvpTfLAhETsbNfOv7cUtQ8NkaKqweqdzy7jhox0UVNSw5I4hTOjhZ+6QRAfLLqnirs/2cDSjhBg/F967aQC9g9ybf6EQnURRRQ3zluzmUHox1/QL5IOb4lCr5ftdmFZpVS1zPtpBfFYpj06M4ckre5g7pC5DOvZdxJ8JuTzy1QGKKmq5eWgYL1/XG1tZzkQ0YeWRszzz/WHKquu4bkAQr83si7O9rJYgrFNGUSVz/rOdzOIq/u+antw9Ru5gdVUVNXUs+OU43+xNw1aj4qkre3DPmCg00vkRnVx6YQV3f7aX+KxSrukbyDs3DsDORs4DRfs4W1zJzA+3k1VSxROTuvPYpG7mDqlLkI69lVMUhf9tOcM/V8ejUqn429Wx3DU6Uu7AimYl55Xz4Jf7OX62hChfZ/5960BiA9zMHZYQJpWYU8adn+4mraCSRybG8JTcWRDAqiNneW7FEYora+kf6sFb1/eTaWui09p8KpfHvq6/uTNnUAhvzO4nF6tEuzuTW8bNi3eSXVLNwxNieOrK7tL/aGfSsbdiOaVV/O2HI/wRn4OXsx2LboljZLSPucMSnUhVrZaXfzvO8l2pONiqefm6PtwwONTcYQlhEttP5/HAF/sprqzlvrFRPHd1rJx0CIOckipe+Oko645nY6dR89ikbtw3NgobGe0mOoniylreWBXPV7tT0ajl5o7oeGdyy7hl8S6ySqq4tn8Qb17fT+rXtKMu27FfnbSaNclrzB1Gu1AUyMz24+DxWGpq7fDyKGJIvyM4OVabO7R2c1XEVUyJnGLuMKzWTwcyeP7HI1TUaJneP4gF03vj6Wxn7rBEB7KmnKnVqTiRGE1CUjgA/XueJCos3cxRtR/Jj22nKAq/HMrkpV+OUVhRS59gN968vj89A2X0krBcVbVavtyVyn82JZJXVkOEtxNvzunPkAgvs8ZlTd8jouUqq+zZeaA/RSVuuLmUMrjfMdxdy8wdllV+N3bZSbNaRUutrtbcYZhcaZkLR0/2JL/AB5VKR2zMSaIjzqBSQa0VrzqhVaSCcXuaERdMn2B3Hl6+n18OZbL9dB7zr+3NtH6BcuW/i7CGnKkokJPny4mEWMrKXXCwr6J/78P4eudLfhSNUqlUXDcgmJHRPsz/5Sgrj2Rx7QdbeWhCDA9NiJE5ysKi5JVV8+3eND7dlkxOaTX2NmoenhDDwxNjLOIuqTV8j4jWs7GrZfjgnRw50ZuMs8Fs3DGU6IgzxEScwcbGfN9P1vjd2GXv2P9+5ndWJa0ydxgmU1LqSmJSFJnZgYAKb898evc4jpsJr4h99/B3JmvL1DzsPfCw9zB3GBZp165dJmurpk7HvzclsmhDInU6hX4h7jx2RTfG9/CT+XpWrrPnzJJSV04k9CA33xeAkKB0enU/gZ1t3WW3bcm5ESQ/guny4MojZ3nxp6Pkl9cQG+DK36/txYgob7nAKcymvLqOzady+f3IWdYdy6ZGq8PORs0tQ8N4cHw0fm4OJj3esGHD2vzaouoiiqqLTBeM6BBzFs0xWVtns/05cqIPNbV22NlWEx2RRFhwGrYm+C5urasjr+aaqGs6/LjtqcvesbcGOp2K7Dw/0jJCyMmrX5rJ2amMHtEJBPpnYerzjJz4HNM2aEI5WG5s1uT/27u34CjqPQ/g357puWaSTK7kQgImCEgCRuuIhNUTdaFEqk6xPLgeTyGiiw+WVRYPbJVV1j7srlapb7tVImptydbCgSoeUE+pW0EhqyAI7tHayJFDgCCQmPs9mUvPzH8fJhlyI5lkenq6//l+itRMerrT/et/8/3Pv6dnxqnasG/LajxVW4p3/vsyvrrchX/4z+9RluvG7+4vw29XF+E3K/PgUjP/ygARAPQP+NHSWp3IyDx/H2pWX4Y/d1C3dZg5GwHmo562ry/FpqoC/POfLuGTH9vxhw+/w4OVfuzatAJP1pTw20Mo7YQQuN4zim+udOPM1R5809KDUCR+ydHyPA/+8HAl/v43FSj0udKy/gsXLqTl79LSULqsE4X5vbh6owqtN1fi55a1uHJ9FSrKbmN5WRtys4d0H78sJeyBLCYWU9A3kIeOrmVo7yxFOBwP7pzsIay65xpKi/Uf0BNNt6YkG/+x5yH8+WY//uvcL/is+Ve8//V1vP/1dTjtNqwu8aGmNBc15TmoKctFTVmOKS4DpKUhGHKhvbMEbe3lGByOfw95TvYg7r3nGkqKO5mRlJL8LCf+7fcP4PcPVeJA01V809KDP98cgMfxEx5fW4S/WVWIzdWFWFng5Sv5pIv+0TDOXuvBN1d6cOZqD9oGAonHyv0ePFVbgqfWl+CBijx+Lz2ZnsMRwX33XkFV5Q3cuF2JX26twI1bK3Hj1kpkZw2jrORXFBd1Icc3zP56gTiwN7FYTEEo7EIg4EH/YC76B/PQ258PTYt/aJndHkFl+U1UlN+GP2cw7Qd/8dri9K4gBbzUNDMerMzDg5V5+JcdNTh7tRf/c6Ub//tLH/7SPoSf2oaA7+PzqTYF95Xm4P6KXNRV5KGuwo+qwiw+AaGUaZqK4VEfhkeyMTScjd7+AoyM+sYfFSjM70HVilYUFfSkLSPNnI0A8zFd6qsLUF9dgMsdQzjxQxs++aEdnzd34PPmDgBAtlvFutIcrCvLwZpl2agu9qG6yId8fvAozWMkFMH/3RrAmavxgXxz2yAm3jjrddrxxNpiPHpvIR69txDVRT5DTyBt3Lhx0cvyUnyazOUKY031VaxaeR2d3cW41V6O7t4i/PXaavz12mq4nEHk+QfgzxmEL2sEXk8AHk8ADtX4y/atgu+xzwAhAC2iIhhyIxh0IxRyxe+H3AgGJ+67EAq7AEwNa6cjjOKiLpQUdaKooAd2u8Sf+LQAMr5PxsqCWhSXO4ZxqX0QzbcH8eOtAVzpHEZsUtrkuFXcX+FHXYUfNWU5KPN7UJrrQX6Wk+/XNyEjMzMWUxCJ2hGJqIhE1fjteGYGAh4Egm4Egh6MjmUhGJr6/lFFiSEvdwDFhd0oL22Hxx00ZJvNjPlojFhM4HLHMM5e7cF3rX34S/sg2gdnHn95Xgeqi+KD/OrirMT95XkefpXeEhDUohgJRTAcjGA4qGFgTEP7QADtAwHc7g/gUvsQrnQNJwbyigJsWO7Ho6viA/kHKvMs+6GNVv+sFkq/YMiJrp5idPUUoaevAJGIY8Y8qqrB6QjD6Ry/dYThdGhwOsNQ1QhUewR2e3T8fvzWbo9AVaNQFAHE/2FL5Vb8beUWaFEBLRpDOBqDFo0hz+vEMp0/m8IofMV+DsMjPrTeXJH4XUCJHwlQ4jdi0vTx3+/Mc2d6LKZAizigaQ5omhNhzYFYbK7LkgVcrhBycwbhdgXhdoeQmz2EfH8/sryjvCyFTM/tsKNufNCO8c/ZGQ1F0NwWH+T/eHMAP94awDct8fcHTud12uFzqfEftwqPww6naoPDboPTboNDtcFhV+BSbbApyvgJAwEhgJiI3/7r39Xy8v8F6hoO4t+/akk8oRRA4v7NIeDWcM2UjLtDuTNp0mNi2onJREaO308M2qcN4ufOxzscjjDy/X3I9g0j2zeC7KwR+HMHeMKTMsJmU7CuLP4K/Uu/rQIQv4T651+H0NI1gmvd4z9do/j+l358/0v/lOUddgX5WU74PU7keh3IcTvgcdrhUm1wqTY4VRtc6vjvDhvs054MTH9uEBNAJBqDFhWIxGKIREXi/nObVuDeZdlp3R8yeub9cxgKRiCEQEwIxCb1OWLa77FJ8wghEI0JjIaiCEfnzieHXcGG8lzUVfjxcFUBNlcXwO/lVR60NLhdYVSW30Zl+W0IAYyOeTEw5MfYmBdjQU/i5L6mOTEWyEppXY0AgC9nTH/l8Wr845NrU/rbmbJkB/Z2xQ6HbeZZoMnCIR9utlXqtk5FicHp0JDlCcDtCsHtDsHjCsHjDsV/H7/vcoZhs93tQoq5t3mpsiscwJldlkvFpqoCbKoqSEzrGAzix1v9uNI5gl8Hg/h1MID+MQ2joQhGghF0D4fQ2juKxVxX9E+/W8eB/QINBTQcPn9zjjn0y8PJFCWWOKvu9gYSZ9xVNQrHpDPuHncIHncQXncQHncQDsdsX1VjH/+hCczHzMnLcmLzqkJsXlU4ZfpIKILW7tE7g/3uEVzvHkX/WBitvaMId6b35NRja4o4sF+E6z2jGBzToCiATVFgG7/FtN+VSfcdNkBRbFAUYFmOG9luFdlux/itihy3A6V+D5b7PSjze7CiwCtt35XMc2+iyZzZGvKyu2d9LBZToGkqQpoT4bADIc0xfoWfPf5CQdQevz/pBQQh7pwELfIWoNhbNPWFI7sN68tzDaxQX0v2UvxkDAU13OwdAxA/CBQoiTAfz/Hxg+PO73ceUxIHjmpXkOtxwOOw84N0iBYoFhMIj18iFY7EL5PSIgLhaBThSPxVEEXBtP+bClYV+3hJ/wIFtShaOuNfkTk5qibuK+Ovtk/s7xnTps2PSTl45zElkZ1eZ/yJrUu1MRuJJglqUQyMaQhFoghF4tkXikQR0mIIjd+f/Nam2Z7JKUr8800cdhtUuwLVFr/SSbXbcE9hFnI9HGAREcmEA3siIiIiIiIiC7Pmp28QEREREREREQAO7ImIiIiIiIgsjQN7IiIiIiIiIgvjwJ6IiIiIiIjIwjiwJyIiIiIiIrIwDuyJiIiIiIiILIwDeyIiIiIiIiILUzO9AakSQiAcDmd6M4hIAk6nE4qiZHozdMN8JCK9yJaPADOSiPRhlny0/MA+HA7jrbfeyvRmEJEEXnvtNbhcrkxvhm6Yj0SkF9nyEWBGEpE+zJKPihBCZHojUrGYs60dHR04dOgQ9uzZg5KSkjRtWeaxTvkslVozVadZzrjqRa9Xo2Q/7mSuT+baALnrM1ttsuUjkFxGmq0drIr7UR/cj/rQez+aJR8t/4q9oigLPkPidDoTt2Y4u5IurFM+S6XWpVJnui0mH2cje3vIXJ/MtQFy1ydzbWaRTEayHfTB/agP7kd9yLof+eF5RERERERERBa2JAf2Pp8PDQ0N8Pl8md6UtGKd8lkqtS6VOq1C9vaQuT6ZawPkrk/m2qyE7aAP7kd9cD/qQ9b9aPn32BMREREREREtZUvyFXsiIiIiIiIiWXBgT0RERERERGRhHNgTERERERERWZh0A/uRkRHs27cPZWVlcLvdqKurw7Fjx5JevqurC3v27EFhYSG8Xi/q6+vx1VdfzZjvscceg6IoM362bdumZzkp1ZNsLQDw5Zdfor6+Hl6vF4WFhdizZw+6urr0LGVORtRpVJvNZbF13r59G/v27UNDQwP8fj8URcGhQ4fuOn+m2xMwplYztKnVyZCZsuekzPkoeyYyB80tlf9bVjkGjSBDP2Ik2fsso8jcNy6akMzWrVuF3+8XBw8eFKdOnRJ79+4VAMSRI0fmXTYYDIra2lqxfPlycfjwYdHY2Ch27NghVFUVTU1NU+ZtaGgQVVVV4ty5c1N+fv75Z1PUs5BampqahKqqYseOHaKxsVEcPnxYlJeXi9raWhEMBnWt526MqNOoNpvLYus8ffq0KCwsFFu2bBHPPvusACA++uijWec1Q3sKYUytZmhTq5MhM2XPSZnzUfZMZA6aWyr5Z5Vj0Agy9CNGkr3PMorMfeNiSTWw/+yzzwQA8cc//nHK9K1bt4qysjIRiUTmXP7dd98VAMS3336bmKZpmli3bp3YuHHjlHkbGhpETU2Nfhs/i1TqWUgtDz30kFi3bp3QNC0x7ezZswKAOHDggE7V3J1RdRrRZnNJpc5oNJq4f/HixTmfQGS6PYUwrtZMt6nVyZCZsuekzPkoeyYyB80t1fyzwjFoBBn6ESPJ3mcZRea+MRVSXYp/4sQJ+Hw+PP3001Omv/DCC2hvb8d333037/Jr1qxBfX19Ypqqqti1axcuXLiAtra2tGz3XNuz2HqSraWtrQ0XL17Ec889B1VVE/Nu3rwZq1evxokTJ3SuavZtTXedZpBKnTZbcv9VzdCegDG1UupkyEzZc1LmfJQ9E5mD5pZq/lnhGDSCDP2IkWTvs4wic9+YCql6jp9++gn33XfflIMYADZs2JB4fL7lJ+adbflLly5NmX7t2jXk5+dDVVVUV1fj9ddfRyAQSKWEGduz2HqSrWXib9xt3vn2mR6MqHNCuttsLqken8muY/LfnL4eI9pzYjvSXeuETLap1cmQmbLnpMz5KHsmMgfNzaj2MUu/nC4y9CNGkr3PMorMfWMq1PlnsY7e3l5UVVXNmJ6fn594fL7lJ+adb/lHHnkEzzzzDNauXYtAIIAvvvgC77zzDs6cOYPTp0/rcrY9lXqSrWXi9m7zzrfP9GBEnYAxbTaXVI/PZNcx+W9OX48R7TmxHemuFch8m1qdDJkpe07KnI+yZyJz0NyMah+z9MvpIkM/YiTZ+yyjyNw3psK0A/umpiY8/vjjSc37ww8/oK6uDgCgKMpd55vrsWTmmfzYG2+8MeWx7du3Y+XKldi/fz8++eQT7Ny5c951JSOVehay7N3mTWaf6cGIOo1qs7mkenymuh6j2nO+dem1HWZoU7NYypkpe07KnI+yZyJz0BiZyr+FMEO/PJ+l3I8YSfY+yygy942LZdqB/Zo1a/Dhhx8mNW9lZSUAoKCgYNYzNH19fQBmP3M1WarL79q1C/v378f58+d1aehUtifZZQsKCgDMfmarr69v3pr1YESdd6N3m80l1W1Ndh1AZttzYjvSXevdGNmmZrJUM1P2nJQ5H2XPROagcTKRf8kyS7+cjKXajxhJ9j7LKDL3jakw7cC+tLQUe/fuXdAy69evx9GjRxGJRKa856K5uRkAUFtbO+/yE/NOluzyE/S6LCOVepKtZeK2ubkZ27dvnzFvsjWnwog652PEpTSpHp/JMEN7AsbUOh+zXR6Vbks1M2XPSZnzUfZMZA4aJxP5lyyz9MvJWKr9iJFk77OMInPfmJJMfyy/nj7//HMBQBw7dmzK9G3btiX1lRsHDhwQAMT58+cT0zRNEzU1NeLhhx+ed/1vv/22ACA+/vjjxRUwTSr1LKSWjRs3itra2il/79y5cwKAeO+993SpZS5G1TkbvdtsLqkenxPm+1qdTLenEMbVOhsj29TqZMhM2XNS5nyUPROZg+amV/sIYd5j0Agy9CNGkr3PMorMfWMqpBrYCxH//sK8vDzxwQcfiFOnTomXXnpJABCHDx+eMt+LL74o7Ha7uHHjRmJaMBgUNTU1oqKiQhw5ckScPHlS7Ny5U6iqKpqamhLzff311+LJJ58UBw8eFI2NjeLTTz8VL7/8srDb7eKJJ56Y8t2mRtSTSi1CCHH69GmhqqrYuXOnOHnypDhy5IioqKgQtbW1IhgM6lZLJus0ss3SUacQQhw/flwcP348ESivvPJKYtpkZmhPIdJfq1na1OpkyEzZc1LmfJQ9E5mD5pZK/glhjWPQCDL0I0aSvc8yisx942JJN7AfHh4Wr776qigpKRFOp1Ns2LBBHD16dMZ8zz//vAAgWltbp0zv6OgQu3fvFvn5+cLtdotNmzaJkydPTpmnpaVFbN++XZSXlwuXyyXcbrdYv369ePPNN3X/z5JMPanUMqGxsVFs2rRJuN1ukZ+fL3bv3i06Ozt1rWUu6a7TyDabSyp1Arjrz3SZbk8h0l+rWdrU6mTITNlzUuZ8lD0TmYPmlmr+WeEYNIIM/YiRZO+zjCJz37hYihBCzHaJPhERERERERGZnwnf9U9EREREREREyeLAnoiIiIiIiMjCOLAnIiIiIiIisjAO7ImIiIiIiIgsjAN7IiIiIiIiIgvjwJ6IiIiIiIjIwjiwJyIiIiIiIrIwDuyJiIiIiIiILIwDeyIiIiIiIiIL48CeiIiIiIiIyMI4sCciIiIiIiKyMA7siYiIiIiIiCzs/wG2cZ/Wqp4vTwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义 ROPE 区间，根据研究的需要指定实际等效范围\n",
    "rope_interval = [-0.05, 0.05]\n",
    "\n",
    "# 绘制后验分布，显示 HDI 和 ROPE\n",
    "az.plot_posterior(\n",
    "    model2_trace,\n",
    "    var_names=[\"beta_1\", \"beta_2\", \"beta_3\"],\n",
    "    hdi_prob=0.95,\n",
    "    rope=rope_interval,\n",
    "    figsize=(12, 3),\n",
    "    textsize=12\n",
    ")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用贝叶斯因子进行差异检验\n",
    "\n",
    "- $beta_3$ 的 $BF_{01}$ 接近30，表明有较强的证据说明不同匹配条件下 $Y$ 的均值相同。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [Y_obs, beta_0, beta_1, beta_2, beta_3, sigma]\n",
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x350 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 进行贝叶斯因子计算，需要采样先验分布\n",
    "with model2:\n",
    "    model2_trace.extend(pm.sample_prior_predictive(5000, random_seed=84735) )\n",
    "\n",
    "fig, axes = plt.subplots(1,3, figsize=(12, 3.5))\n",
    "\n",
    "# 绘制贝叶斯因子图\n",
    "# beta1\n",
    "ax = axes[0]\n",
    "az.plot_bf(model2_trace, var_name=\"beta_1\", ref_val=0, ax=ax)\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "# beta2\n",
    "ax = axes[1]\n",
    "az.plot_bf(model2_trace, var_name=\"beta_2\", ref_val=0, ax=ax)\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "# beta3\n",
    "ax = axes[2]\n",
    "az.plot_bf(model2_trace, var_name=\"beta_3\", ref_val=0, ax=ax)\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "\n",
    "# 去除上框线和右框线\n",
    "sns.despine()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**后验预测**\n",
    "\n",
    "最后，我们可以使用 `pm.sample_posterior_predictive` 函数来生成后验预测。\n",
    "\n",
    "并通过 `az.plot_ppc` 函数来绘制后验预测的基本结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [Y_obs]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "60a3c31376764f30a3bd705c7c5fd726",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model2:\n",
    "    model2_ppc = pm.sample_posterior_predictive(model2_trace, random_seed=84735) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Y_obs'>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_ppc(model2_ppc, num_pp_samples = 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import xarray as xr\n",
    "\n",
    "# 导入真实的自变量\n",
    "X1 = xr.DataArray((df['Label'] == 'Friend').astype(int))\n",
    "X2 = xr.DataArray((df['Label'] == 'Stranger').astype(int))\n",
    "Matching = xr.DataArray((df['Matching'] == 'matching').astype(int))\n",
    "\n",
    "model2_trace.posterior[\"y_model\"] = model2_trace.posterior[\"beta_0\"] + model2_trace.posterior[\"beta_1\"] * X1 + model2_trace.posterior[\"beta_2\"] * X2 + model2_trace.posterior[\"beta_3\"] * Matching\n",
    "\n",
    "df[\"model2_prediction\"] = model2_trace.posterior.y_model.mean(dim=[\"chain\",\"draw\"]).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# 在第一个子图上绘制 Model 1 的预测结果\n",
    "plot_prediction(df, predicted_y=\"model1_prediction\", ax=axes[0])\n",
    "axes[0].set_title(\"Model 1\")\n",
    "\n",
    "# 在第二个子图上绘制 Model 2 的预测结果\n",
    "plot_prediction(df, predicted_y=\"model2_prediction\", ax=axes[1])\n",
    "axes[1].set_title(\"Model 2\")\n",
    "\n",
    "# 显示图形\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从模型预测结果来看：\n",
    "- 模型一中，不同匹配条件下的反应时预测相同；但在模型二中，不同匹配条件下的反应时预测不同，说明匹配条件对反应时存在影响。\n",
    "- 但在模型二中，无论标签如何，模型预测的匹配效应相同，这是因为模型二没有考虑标签“Label”和匹配条件“Matching”的交互作用。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型三：带交互项的2 X 3 的多元线性回归  \n",
    "\n",
    "\n",
    "**交互作用：** 当模型存在两个或两个以上的自变量时，交互作用是指一个自变量$X_1$对因变量$Y$的影响会随着自变量$X_2$不同水平的变化而有所差异。\n",
    "\n",
    "当我们考虑交互效应时，模型不仅包含 “Label” 和 “Matching” 的独立主效应，还需要加入它们之间的交互作用。\n",
    "\n",
    "加入交互项可以观察 “Label” 和 “Matching” 是否存在相互依赖的影响，即 “Matching” 对 “Self、Friend 和 Stranger” 条件的影响是否不同。\n",
    "\n",
    "通过引入交互项，我们能够捕捉变量之间的相互关系。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**多个理解变量下，不同编码和研究效应的关系**\n",
    "\n",
    "如图所示，表中列出了 Treatment Coding 和 Sum Coding 两种常用的因子变量编码方式，并展示了它们在研究主效应和交互效应时的特点：\n",
    "\n",
    "<div style=\"text-align: center;\">\n",
    "    <img src=\"https://pic3.zhimg.com/80/v2-f95e51b7e6e26feab9ca91077d9c244e_1440w.webp\" \n",
    "         alt=\"Image Description\" \n",
    "         style=\"width: 80%; height: auto;\">\n",
    "</div>\n",
    "\n",
    "> 参考资料：\n",
    "> [线性（混合）模型中如何对因子变量事先生成虚拟变量 - 知乎](https://zhuanlan.zhihu.com/p/103547646)\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 哑变量编码规则\n",
    "\n",
    "增加了交互效应后的线性模型的编码规则应该是：\n",
    "\n",
    "1. **主效应的编码规则：**\n",
    "   - **Label (3 levels):**\n",
    "     - $( X_{L1} = 1)$ 表示 \"Friend\" 条件；$( X_{L1} = 0 )$ 表示其他条件;\n",
    "     - $( X_{L2} = 1 )$ 表示 \"Stranger\" 条件；$( X_{L2} = 0 )$ 表示其他条件;\n",
    "     - $( Self)$ 为基线水平，不需要单独编码（隐含在 $( X_{L1} = 0, X_{L2} = 0)$ 中）。\n",
    "\n",
    "   - **Matching (2 levels):**\n",
    "     - $( X_{M1} = 1)$ 表示 \"nonmatching\" 条件；\n",
    "     - $( X_{M1} = 0 )$ 表示 \"matching\" 条件（基线水平）。\n",
    "\n",
    "2. **交互项的编码规则：**\n",
    "   - **交互项 $( X_{L1} \\cdot X_{M1} )$:**\n",
    "     - 当 $( X_{L1} = 1) 且 ( X_{M1} = 1)$ 时，交互项 $( X_{L1} \\cdot X_{M1} = 1)$。\n",
    "     - 否则，$( X_{L1} \\cdot X_{M1} = 0 )$。\n",
    "\n",
    "   - **交互项 $( X_{L2} \\cdot X_{M1})$:**\n",
    "     - 当 $( X_{L2} = 1)$ 且 $( X_{M1} = 1)$ 时，交互项 $( X_{L2} \\cdot X_{M1} = 1)$。\n",
    "     - 否则，$( X_{L2} \\cdot X_{M1} = 0)$。\n",
    "\n",
    "**Treatment编码矩阵**\n",
    "\n",
    "\n",
    "| Label     | Matching    | 截距 (baseline) | $X_{L1}$ | $X_{L2}$ | $X_{M1}$ | $X_{L1} \\cdot X_{M1}$  | $X_{L2} \\cdot X_{M1}$ |\n",
    "|-----------|-------------|-----------------|--------------|--------------|--------------|---------------------------|---------------------------|\n",
    "| Self      | matching    | 1               | 0            | 0            | 0            | 0                         | 0                         |\n",
    "| Self      | nonmatching | 1               | 0            | 0            | 1            | 0                         | 0                         |\n",
    "| Friend    | matching    | 1               | 1            | 0            | 0            | 0                         | 0                         |\n",
    "| Friend    | nonmatching | 1               | 1            | 0            | 1            | 1                         | 0                         |\n",
    "| Stranger  | matching    | 1               | 0            | 1            | 0            | 0                         | 0                         |\n",
    "| Stranger  | nonmatching | 1               | 0            | 1            | 1            | 0                         | 1                         |\n",
    "\n",
    "\n",
    "<div style=\"padding-bottom: 80px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型设定\n",
    "\n",
    "在了解哑变量之后，我们就可以开始进行模型拟合和推断了。\n",
    "\n",
    "有交互项的 2 X 3 的线性回归模型表达为：\n",
    "\n",
    "$$\n",
    "Y = \\beta_0 + \\beta_1 \\cdot X_{L1} + \\beta_2 \\cdot X_{L2} + \\beta_3 \\cdot X_{M1} + \\beta_4 \\cdot (X_{L1} \\cdot X_{M1}) + \\beta_5 \\cdot (X_{L2} \\cdot X_{M1}) + \\epsilon_i\n",
    "$$\n",
    "\n",
    "在这个模型中：\n",
    "\n",
    "- $ X_{L1} \\cdot X_{M1} $ 表示在“Label”条件中 “Friend” 水平和 “Matching” 条件中和“nonmatching” 水平的交互作用。\n",
    "\n",
    "- $ X_{L2} \\cdot X_{M1} $ 表示在“Label”条件中 “stranger” 水平和 “Matching” 条件中和“nonmatching”水平的交互作用。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**模型先验设置**\n",
    "\n",
    "现在我们的线性模型中增加了交互效应，那么我们需要对$\\beta_4$ 和 $\\beta_5$设置先验分布，即：\n",
    "\n",
    "- $\\beta_4$ 和 $\\beta_5$ ： \n",
    "$$ \\beta_4 \\sim N(0, 1^2), \\quad \\beta_5 \\sim N(0, 1^2) $$\n",
    "\n",
    "- $\\beta_0$： \n",
    "$$ \\beta_0 \\sim N(5, 2^2) $$\n",
    "\n",
    "- $\\beta_1$ , $\\beta_2$ 和$\\beta_3$：\n",
    "$$ \\beta_1 \\sim N(0, 1^2),  \\beta_2 \\sim N(0, 1^2)  , \\beta_3 \\sim N(0, 1^2) $$\n",
    "\n",
    "- $\\sigma$： \n",
    "$$ \\sigma \\sim Exp(0.3) $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先验设置：\n",
    "\n",
    "* > $Y_i \\sim N\\left(\\mu_i, \\sigma^2\\right)$\n",
    "\n",
    "* > $\\sigma \\sim \\text{Exp}(0.3)$\n",
    "\n",
    "* > $\\beta_0 \\sim N\\left(5, 2^2\\right)$\n",
    "\n",
    "* > $\\beta_1 \\sim N\\left(0, 1^2\\right)$\n",
    "\n",
    "* > $\\beta_2 \\sim N\\left(0, 1^2\\right)$\n",
    "\n",
    "* > $\\beta_3 \\sim N\\left(0, 1^2\\right)$\n",
    "\n",
    "* > $\\beta_4 \\sim N\\left(0, 1^2\\right)$\n",
    "\n",
    "* > $\\beta_5 \\sim N\\left(0, 1^2\\right)$\n",
    "\n",
    "定义回归模型：\n",
    "\n",
    "* > $\\mu_i = \\beta_0 + \\beta_1 X_{L1} + \\beta_2 X_{L2} + \\beta_3 X_{M1} + \\beta_4 (X_{L1} \\cdot X_{M1}) + \\beta_5 (X_{L2} \\cdot X_{M1})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型拟合和推断\n",
    "\n",
    "我们可以通过 PyMC 构建该模型，并使用 MCMC 算法进行采样。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 转换分类变量为哑变量\n",
    "X1 = (df['Label'] == 'Friend').astype(int)\n",
    "X2 = (df['Label'] == 'Stranger').astype(int)\n",
    "\n",
    "# Matching 条件的哑变量\n",
    "Matching = (df['Matching'] == 'matching').astype(int)  \n",
    "\n",
    "# Friend 和 Matching 的交互\n",
    "Interaction_1 = X1 * Matching  \n",
    "# Stranger 和 Matching 的交互\n",
    "Interaction_2 = X2 * Matching  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "with pm.Model() as model3:\n",
    "    # 定义先验分布\n",
    "    beta_0 = pm.Normal('beta_0', mu=5, sigma=2)  \n",
    "    beta_1 = pm.Normal('beta_1', mu=0, sigma=1) \n",
    "    beta_2 = pm.Normal('beta_2', mu=0, sigma=1)  \n",
    "    beta_3 = pm.Normal('beta_3', mu=0, sigma=1)  \n",
    "    beta_4 = pm.Normal('beta_4', mu=0, sigma=1) \n",
    "    beta_5 = pm.Normal('beta_5', mu=0, sigma=1)  \n",
    "    sigma = pm.Exponential('sigma', lam=0.3)  \n",
    "    \n",
    "    # 线性模型\n",
    "    mu = (beta_0 + beta_1 * X1 + beta_2 * X2 + beta_3 * Matching +\n",
    "          beta_4 * Interaction_1 + beta_5 * Interaction_2)\n",
    "    \n",
    "    # 观测数据的似然函数\n",
    "    likelihood = pm.Normal('Y_obs', mu=mu, sigma=sigma, observed=df['RT_sec'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**进行后验采样**\n",
    "\n",
    "接下来我们使用`pm.sample()`进行mcmc采样  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta_0, beta_1, beta_2, beta_3, beta_4, beta_5, sigma]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0d81859147c945058a7f8949f25b7f56",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 7 seconds.\n"
     ]
    }
   ],
   "source": [
    "with model3:\n",
    "    model3_trace = pm.sample(draws=5000,                   # 使用mcmc方法进行采样，draws为采样次数\n",
    "                             tune=1000,                    # tune为调整采样策略的次数，可以决定这些结果是否要被保留\n",
    "                             chains=4,                     # 链数\n",
    "                             discard_tuned_samples=True,  # tune的结果将在采样结束后被丢弃\n",
    "                             random_seed=84735)           # 后验采样  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**MCMC诊断和后验推断**\n",
    "\n",
    "我们可以使用 `az.summary` 函数来查看诊断和后验推断的摘要。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>beta_0</th>\n",
       "      <td>0.728</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.683</td>\n",
       "      <td>0.774</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7122.0</td>\n",
       "      <td>9651.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_1</th>\n",
       "      <td>0.048</td>\n",
       "      <td>0.034</td>\n",
       "      <td>-0.017</td>\n",
       "      <td>0.111</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8056.0</td>\n",
       "      <td>11444.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_2</th>\n",
       "      <td>0.032</td>\n",
       "      <td>0.034</td>\n",
       "      <td>-0.033</td>\n",
       "      <td>0.096</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7943.0</td>\n",
       "      <td>10889.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_3</th>\n",
       "      <td>-0.051</td>\n",
       "      <td>0.034</td>\n",
       "      <td>-0.116</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7127.0</td>\n",
       "      <td>10338.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_4</th>\n",
       "      <td>0.031</td>\n",
       "      <td>0.048</td>\n",
       "      <td>-0.060</td>\n",
       "      <td>0.122</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8148.0</td>\n",
       "      <td>12242.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_5</th>\n",
       "      <td>0.058</td>\n",
       "      <td>0.048</td>\n",
       "      <td>-0.032</td>\n",
       "      <td>0.149</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8253.0</td>\n",
       "      <td>11786.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.133</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.120</td>\n",
       "      <td>0.147</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15559.0</td>\n",
       "      <td>12979.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "beta_0  0.728  0.024   0.683    0.774      0.000      0.0    7122.0    9651.0   \n",
       "beta_1  0.048  0.034  -0.017    0.111      0.000      0.0    8056.0   11444.0   \n",
       "beta_2  0.032  0.034  -0.033    0.096      0.000      0.0    7943.0   10889.0   \n",
       "beta_3 -0.051  0.034  -0.116    0.012      0.000      0.0    7127.0   10338.0   \n",
       "beta_4  0.031  0.048  -0.060    0.122      0.001      0.0    8148.0   12242.0   \n",
       "beta_5  0.058  0.048  -0.032    0.149      0.001      0.0    8253.0   11786.0   \n",
       "sigma   0.133  0.007   0.120    0.147      0.000      0.0   15559.0   12979.0   \n",
       "\n",
       "        r_hat  \n",
       "beta_0    1.0  \n",
       "beta_1    1.0  \n",
       "beta_2    1.0  \n",
       "beta_3    1.0  \n",
       "beta_4    1.0  \n",
       "beta_5    1.0  \n",
       "sigma     1.0  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(model3_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 ROPE+HDI 对参数进行检验\n",
    "\n",
    "- 可以看到，$beta_4$ 和 $beta_5$ 非常接近0，表明没有交互效应。 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义 ROPE 区间，根据研究的需要指定实际等效范围\n",
    "rope_interval = [-0.05, 0.05]\n",
    "\n",
    "# 绘制后验分布，显示 HDI 和 ROPE\n",
    "az.plot_posterior(\n",
    "    model3_trace,\n",
    "    var_names=[\"beta_4\", \"beta_5\"],\n",
    "    hdi_prob=0.95,\n",
    "    rope=rope_interval,\n",
    "    figsize=(12, 3),\n",
    "    textsize=12\n",
    ")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用贝叶斯因子进行差异检验\n",
    "\n",
    "- $beta_4$ 和 $beta_5$ 的 $BF_{01}$z 在10～20之间，表明有证据说明不存在交互作用。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [Y_obs, beta_0, beta_1, beta_2, beta_3, beta_4, beta_5, sigma]\n",
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 进行贝叶斯因子计算，需要采样先验分布\n",
    "with model3:\n",
    "    model3_trace.extend(pm.sample_prior_predictive(5000, random_seed=84735) )\n",
    "\n",
    "fig, axes = plt.subplots(1,2, figsize=(9, 3.5))\n",
    "\n",
    "# 绘制贝叶斯因子图\n",
    "# beta4\n",
    "ax = axes[0]\n",
    "az.plot_bf(model3_trace, var_name=\"beta_4\", ref_val=0, ax=ax)\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "# beta5\n",
    "ax = axes[1]\n",
    "az.plot_bf(model3_trace, var_name=\"beta_5\", ref_val=0, ax=ax)\n",
    "ax.set_xlim(-0.5, 0.5) \n",
    "\n",
    "# 去除上框线和右框线\n",
    "sns.despine()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**后验预测**\n",
    "\n",
    "最后，我们可以使用 `pm.sample_posterior_predictive` 函数来生成后验预测。\n",
    "\n",
    "并通过 `az.plot_ppc` 函数来绘制后验预测的基本结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [Y_obs]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9595fc1174b74eb79230c3d90667215d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model3:\n",
    "    model3_ppc = pm.sample_posterior_predictive(model3_trace, random_seed=84735) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Y_obs'>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_ppc(model3_ppc, num_pp_samples = 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import xarray as xr\n",
    "\n",
    "# 导入真实的自变量\n",
    "X1 = xr.DataArray((df['Label'] == 'Friend').astype(int))\n",
    "X2 = xr.DataArray((df['Label'] == 'Stranger').astype(int))\n",
    "Matching = xr.DataArray((df['Matching'] == 'matching').astype(int))\n",
    "Interaction_1 = X1 * Matching\n",
    "Interaction_2 = X2 * Matching\n",
    "\n",
    "model3_trace.posterior[\"y_model\"] = model3_trace.posterior[\"beta_0\"] + \\\n",
    "    (model3_trace.posterior[\"beta_1\"] * X1) + \\\n",
    "    (model3_trace.posterior[\"beta_2\"] * X2) + \\\n",
    "    (model3_trace.posterior[\"beta_3\"] * Matching) + \\\n",
    "    (model3_trace.posterior[\"beta_4\"] * Interaction_1) + \\\n",
    "    (model3_trace.posterior[\"beta_5\"] * Interaction_2)\n",
    "\n",
    "df[\"model3_prediction\"] = model3_trace.posterior.y_model.mean(dim=[\"chain\",\"draw\"]).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Label'] = df['Label'].astype(str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# 绘制model3预测结果\n",
    "plot_prediction(df, \"model3_prediction\", ax=axes[0])\n",
    "axes[0].set_title(\"Model 3\")\n",
    "\n",
    "# 绘制model2预测结果\n",
    "plot_prediction(df, \"model2_prediction\", ax=axes[1])\n",
    "axes[1].set_title(\"Model 2\")\n",
    "\n",
    "# 显示图像\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[<Axes: title={'center': 'Model 3'}, xlabel='beta_4', ylabel='Density'>\n",
      " <Axes: title={'center': 'Model 2'}, xlabel='beta_5', ylabel='Density'>]\n"
     ]
    }
   ],
   "source": [
    "print(axes)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "相较于模型2，模型3考虑了匹配条件与标签之间的交互作用，因此可以更准确地捕捉反应时间随标签和匹配条件变化的非线性关系。\n",
    "\n",
    "- 具体表现为，在 “stranger” 条件下，匹配条件对反应时间几乎没有影响。模型3能够捕捉到这一特性，而模型2则不能。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型解读与结论\n",
    "\n",
    "通过贝叶斯回归模型的后验分布，我们可以推断以下几个方面：\n",
    "- **反应时间与标签的关系**：根据 $\\beta_1$  和  $\\beta_2$ 的估计值，我们可以判断不同标签条件下反应时间的差异（自我对比其他标签）。\n",
    "- **匹配条件的影响**：通过 $\\beta_1$，我们可以判断是否匹配条件会显著影响反应时间。\n",
    "- **交互效应**：通过 $\\beta_4$ 和 $\\beta_5$ 的估计，我们可以了解匹配条件与标签之间的交互作用是否显著，尤其是在自我与他人标签的反应时间是否有显著差异。\n",
    "\n",
    "思考题：贝叶斯回归模型与传统的线性回归模型得到的结论是否一致？\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_id": "59F55A34294640119090B2CD91EDA820",
    "id": "878F5F69394341388D340773D2963CFD",
    "jupyter": {},
    "notebookId": "655b69f19f41eb29b96aa415",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 练习\n",
    "\n",
    "在以下的练习中，我们需要采用上述的思路，在另一个问题情境下使用贝叶斯的线性回归来解决问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 背景介绍\n",
    "\n",
    "> * 🤦‍♀️🤦‍♀️当你压力大时，或许也曾：疯狂购物、沉迷游戏；但有的时候，当你感觉到压力大时，或许也曾：卸载软件，聚精会神  \n",
    "> * 从直觉上我们能感受到似乎压力与自我控制之间存在某种联系  \n",
    "\n",
    "我们使用的数据来自Human Penguin Project (Hu et al., 2018, doi: 10.17605/OSF.IO/H52D3)，该项目使用了多种常见的心理测量量表，并在跨国人群中进行施测，其中包含了测量压力与自我控制的量表。  \n",
    "\n",
    "- 测量压力的量表共有14道题，每道题的标尺有5个水平，分值为1-5，总分的分布范围为14-70  \n",
    "\n",
    "- 测量自我控制的量表共有13道题，每道题的标尺有5个水平，分值为1-5，总分的分布范围为13-65  \n",
    "\n",
    "> * 数据来源: Hu, C.-P. et al. (2018). Raw data from the Human Penguin Project. Open Science Framework. https://doi.org/10.17605/OSF.IO/H52D3  \n",
    "> * 压力量表来源：Cohen, S., Kamarck, T. & Mermelstein, R. A global measure of perceived stress. J. Health. Soc. Behav. 24, 385–396 (1983).  \n",
    "> * 自我控制量表来源：Tangney, J. P., Baumeister, R. F. & Boone, A. L. High self-control predicts good adjustment, less pathology, better grades, and interpersonal success. J. Pers. 72, 271–324 (2004)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**使用线性模型表示二者关系**  \n",
    "\n",
    "* 在这个例子中，我们将每个被试的自我控制水平设为$Y$，压力水平设为$X$。在收集完n个被试的数据后，我们可以得到：  \n",
    "\n",
    "$$  \n",
    "\\left\\lbrace (Y_1,X_1), (Y_2,X_2),...,(Y_n,X_n) \\right\\rbrace  \n",
    "$$  \n",
    "\n",
    "* 我们可以使用线性模型来描述$Y$与$X$的关系，常见地，我们会将二者的关系写为：  \n",
    "\n",
    "$$  \n",
    "Y_i = \\beta_0 + \\beta_1 X_{i1} + \\epsilon \\;\\;\\;\\;\\;\\;\\;\\;\\epsilon \\sim N(0,\\sigma^2)\\\\  \n",
    "$$  \n",
    "\n",
    "*($\\beta_0$为截距，$\\beta_1$为斜率，$\\epsilon$为残差)*  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_id": "A932777D911B4CA2970DD761F950B222",
    "id": "195E468E885B4A18B404B8FECF51A61A",
    "jupyter": {},
    "notebookId": "655b69f19f41eb29b96aa415",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "#### 模型4定义  \n",
    "\n",
    "现在，我们可以为参数$(\\beta_0, \\beta_1, \\sigma)$设置先验： \n",
    "\n",
    "* > $Y_i {\\sim} N\\left(\\mu_i, \\sigma^2\\right)$  \n",
    "\n",
    "* > $\\sigma   \\sim \\text{Exp}(0.6)$  \n",
    "  \n",
    "* > $\\beta_{0}   \\sim N\\left(50, 10^2 \\right)$  \n",
    "\n",
    "* > $\\beta_1   \\sim N\\left(0, 10^2 \\right)$  \n",
    "  \n",
    "定义回归模型：\n",
    "* > $\\mu_i = \\beta_0 + \\beta_1 X_i$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "_id": "CF0D7F4E507742AA9F5884B7D223867E",
    "collapsed": false,
    "id": "0D94AF6C5EAC4D4E9857D5A5B6F261B1",
    "jupyter": {},
    "notebookId": "655b69f19f41eb29b96aa415",
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": [],
    "trusted": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "import arviz as az"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 通过 pd.read_csv 加载数据 Data_Sum_HPP_Multi_Site_Share.csv\n",
    "try:\n",
    "    df_re = pd.read_csv('/home/mw/input/bayes3797/Data_Sum_HPP_Multi_Site_Share.csv')\n",
    "except:\n",
    "    df_re= pd.read_csv('data/Data_Sum_HPP_Multi_Site_Share.csv')\n",
    "\n",
    "\n",
    "# 筛选站点为\"Tsinghua\"的数据\n",
    "df = df_re[df_re[\"Site\"] == \"Tsinghua\"]\n",
    "\n",
    "df = df[[\"stress\",\"scontrol\",\"smoke\"]]\n",
    "\n",
    "#1 表示吸烟，2表示不吸烟\n",
    "df[\"smoke\"] =  np.where(df['smoke'] == 2, 0, 1)\n",
    "df[\"smoke_recode\"] =  np.where(df['smoke'] == 1, \"yes\", \"no\")\n",
    "\n",
    "\n",
    "#设置索引\n",
    "df[\"index\"] = range(len(df))\n",
    "df = df.set_index(\"index\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务1：根据数据和模型定义 PyMC 模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model4:\n",
    "    \n",
    "    ##---------------------------\n",
    "    #     定义参数先验，包括 beta_0，beta_1，sigma\n",
    "    #---------------------------\n",
    "    beta_0 = ...          \n",
    "    beta_1 = ...\n",
    "    sigma = ...\n",
    "\n",
    "\n",
    "    x = pm.MutableData(\"x\",df.stress)                    #x是自变量压力水平\n",
    "    ##---------------------------\n",
    "    #     定义回归模型\n",
    "    #---------------------------\n",
    "    mu = ...                              \n",
    "\n",
    "    ##---------------------------\n",
    "    #     定义似然函数\n",
    "    #---------------------------\n",
    "    likelihood = ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务2：拟合模型并进行 MCMC 检查"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta_0, beta_1, sigma]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c1d58f856aea4c64a4a25668a3e6096d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 6 seconds.\n"
     ]
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     对模型 model4 进行 MCMC 采样\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     通过可视化+统计指标检验 MCMC 是否收敛，当你顺利运行了这段代码，可以举手示意助教/老师帮助你检查其模型建立的是否正确\n",
    "#     提示：可以使用 az.az.plot_trace() 和 az.summary()函数\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务3：使用 HDI 或者 BF 进行模型推断"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     参考前面的代码计算 HDI + ROPE 区间 或者贝叶斯因子计算\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务4：进行后验预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "_id": "E8926B763DD04A4DAA79386771C3C17A",
    "collapsed": false,
    "id": "B41C37A9609B4E71BCECF9FEA6825FB7",
    "jupyter": {},
    "notebookId": "655b69f19f41eb29b96aa415",
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": [],
    "trusted": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [y_est]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7e915738838a42c288ec2127d4bb0bcd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     对模型进行后验预测\n",
    "#---------------------------\n",
    "with model4:\n",
    "    model4_ppc = ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     可视化后验预测结果\n",
    "#     提示：可以使用 az.plot_ppc(...)\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型5：增加预测变量  \n",
    "\n",
    "\n",
    "🤔 是否可以将吸烟情况和压力同时加入到目前的模型4中?  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们现在将吸烟情况加入到目前的模型中的话，我们的线性回归模型则会更新为：\n",
    "\n",
    "$$  \n",
    "Y_i = \\beta_0 + \\beta_1 X_{i1} + \\beta_2 X_{i2} + \\epsilon \\;\\;\\;\\;\\;\\;\\;\\;\\epsilon \\sim N(0,\\sigma^2)\\\\  \n",
    "$$  \n",
    "\n",
    "- $X_{i1}$ 是第$i$个被试的压力水平;\n",
    "- $X_{i2}$ 是第$i$个被试的吸烟状态，$X_{i2} = 0$ 表示不吸烟，$X_{i2} =1$ 表示吸烟;\n",
    "\n",
    "\n",
    "\n",
    "*($\\beta_0$为截距，$\\beta_1$为斜率，$\\epsilon$为残差)*  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**各参数(回归系数)的意义：**  \n",
    "\n",
    "在现在的例子中，自变量包括离散变量和连续变量。  \n",
    "\n",
    "在自变量中，$X_{i2}$为离散变量，`0` 表示不吸烟，`1`表示吸烟  \n",
    "\n",
    "* 当$X_{i2} = 0$时，$\\mu_i = \\beta_0 + \\beta_1X_{i1} + \\beta_2 \\cdot 0 = \\beta_0 + \\beta_1X_{i1}$  \n",
    "\n",
    "    * 表示不吸烟情况下，自我控制分数随压力分数变化的情况，二者的关系可以被简化为一条直线。  \n",
    "\n",
    "* 当$X_{i2} = 1$时，$\\mu_i = \\beta_0 + \\beta_1X_{i1} + \\beta_2 \\cdot 1 = (\\beta_0 + \\beta_2) + \\beta_1X_{i1}$  \n",
    "\n",
    "    * 表示吸烟情况下，自我控制分数随压力分数变化的情况。  \n",
    "\n",
    "> 注意，在该模型中，我们假设在两种吸烟条件下，压力对自我控制的影响是相同的，即不存在吸烟对于压力的调节作用。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在，我们可以结合数据与先验，为参数$(\\beta_0, \\beta_1, \\beta_2, \\sigma)$生成后验模型  \n",
    "\n",
    "* 当后验分布过于复杂时，我们可以使用MCMC来近似后验分布  \n",
    "\n",
    "    * 我们使用PyMC来完成采样过程  \n",
    "\n",
    "\n",
    "我们的先验设置： \n",
    "\n",
    "* > $Y_i {\\sim} N\\left(\\mu_i, \\sigma^2\\right)$  \n",
    "\n",
    "* > $\\beta_{0}   \\sim N\\left(50, 10^2 \\right)$  \n",
    "\n",
    "* > $\\beta_1   \\sim N\\left(0, 10^2 \\right)$  \n",
    "\n",
    "* > $\\beta_2   \\sim N\\left(0, 10^2 \\right)$  \n",
    "\n",
    "* > $\\sigma   \\sim \\text{Exp}(0.6)$  \n",
    "\n",
    "定义回归模型：\n",
    "* > $\\mu_i = \\beta_0 + \\beta_1 X_{1i} + \\beta_2 X_{2i}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务1：根据数据和模型定义 PyMC 模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model5:\n",
    "    ##---------------------------\n",
    "    #     定义参数先验，包括 beta_0，beta_1，sigma\n",
    "    #---------------------------\n",
    "    beta_0 = ...          \n",
    "    beta_1 = ...\n",
    "    beta_2 = ...\n",
    "    sigma = ...\n",
    "\n",
    "\n",
    "    stress = pm.MutableData(\"stress\",df.stress, dims=\"obs_id\")      #stress是自变量压力水平\n",
    "    smoke = pm.MutableData(\"smoke\",df.smoke, dims=\"obs_id\")         #smoke是自变量吸烟水平\n",
    "    ##---------------------------\n",
    "    #     定义回归模型\n",
    "    #---------------------------\n",
    "    mu = pm.Deterministic(\"mu\", ..., dims=\"obs_id\")    #定义mu，自变量与先验结合\n",
    "\n",
    "    ##---------------------------\n",
    "    #     定义似然函数\n",
    "    #---------------------------\n",
    "    likelihood = pm.Normal(\"y_est\", mu=..., sigma=..., observed=..., dims=\"obs_id\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务2：拟合模型并进行 MCMC 检查"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta_0, beta_1, beta_2, sigma]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "80a201d508684dc1b0fa3eefc0a75eb4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 9 seconds.\n"
     ]
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     对模型 model5 进行 MCMC 采样\n",
    "#     注意！！！以下代码可能需要运行1-2分钟左右\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     通过可视化+统计指标检验 MCMC 是否收敛，，当你顺利运行了这段代码，可以举手示意助教/老师帮助你检查其模型建立的是否正确\n",
    "#     提示：可以使用 az.az.plot_trace() 和 az.summary()函数\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务3：使用 HDI 或者 BF 进行模型推断"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     参考前面的代码计算 HDI + ROPE 区间 或者贝叶斯因子计算\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务4：进行后验预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [y_est]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "75803447235140ebbcf65f2dbd52c346",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     对模型进行后验预测\n",
    "#---------------------------\n",
    "with model5:\n",
    "    model5_ppc = ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     可视化后验预测结果\n",
    "#     提示：可以使用 az.plot_ppc(...)\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多元线性回归：增加交互项  \n",
    " \n",
    "现在，我们可以假设，在不同的吸烟状况下，压力对自我控制的影响略有不同(体现在斜率上)  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s49oqb24we.png?imageView2/0/w/960/h/960)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "那么我们可以加入交互项：$\\mu = \\beta_0 + \\beta_1 X_{1} + \\beta_2 X_{2} + \\beta_3 X_{1}X_{2}$  \n",
    "\n",
    "$$  \n",
    "\\begin{equation}  \n",
    "\\begin{array}{lcrl}  \n",
    "\\text{data:} & \\hspace{.05in} & Y_i|\\beta_0,\\beta_1,\\beta_2,\\beta_3,\\sigma & \\stackrel{ind}{\\sim} N(\\mu_i, \\; \\sigma^2) \\;\\; \\text{ with } \\; \\mu_i = \\beta_0 + \\beta_1X_{i1} + \\beta_2X_{i2} + \\beta_3X_{i1}X_{i2} \\\\  \n",
    "\\text{priors:} & & \\beta_{0c}  &  \\sim N\\left(50, 10^2 \\right)  \\\\  \n",
    "                     & & \\beta_1  & \\sim N\\left(0, 10^2 \\right) \\\\  \n",
    "                     & & \\beta_2  & \\sim N\\left(0, 10^2 \\right) \\\\  \n",
    "                     & & \\beta_3  & \\sim N\\left(0, 10^2 \\right) \\\\  \n",
    "                     & & \\sigma & \\sim \\text{Exp}(0.6)  .\\\\  \n",
    "\\end{array}  \n",
    "\\end{equation}  \n",
    "$$  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先验设置如下：\n",
    "\n",
    "* > $Y_i \\sim N\\left(\\mu_i, \\sigma^2\\right)$\n",
    "\n",
    "* > $\\sigma \\sim \\text{Exp}(0.6)$\n",
    "\n",
    "* > $\\beta_0 \\sim N\\left(50, 10^2\\right)$\n",
    "\n",
    "* > $\\beta_1 \\sim N\\left(0, 10^2\\right)$\n",
    "\n",
    "* > $\\beta_2 \\sim N\\left(0, 10^2\\right)$\n",
    "\n",
    "* > $\\beta_3 \\sim N\\left(0, 10^2\\right)$\n",
    "\n",
    "定义回归模型：\n",
    "\n",
    "* > $\\mu_i = \\beta_0 + \\beta_1 X_{i1} + \\beta_2 X_{i2} + \\beta_3 X_{i1}X_{i2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**在这个例子中，各参数的意义：**  \n",
    "\n",
    "* 当$X_{i2} = 0$时，$\\mu_i = \\beta_0 + \\beta_1X_{i1}$  \n",
    "\n",
    "    * 表示不吸烟情况下，自我控制分数随压力分数变化的情况，二者的关系可以被简化为一条直线。  \n",
    "\n",
    "* 当$X_{i2} = 1$时，$\\mu_i = \\beta_0 + \\beta_1X_{i1} + \\beta_2X_{i2} + \\beta_3X_{i1} = (\\beta_0 +\\beta_2) + (\\beta_1 + \\beta_3)X_{i1}$  \n",
    "\n",
    "    * 表示吸烟情况下，自我控制分数随压力分数变化的情况  \n",
    "    * 注意截距项和斜率项的变化  \n",
    "    * 此时压力对自我控制的影响为$(\\beta_1 + \\beta_3)$，体现了吸烟对这一关系的影响  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务1：根据数据和模型定义 PyMC 模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model6:\n",
    "    \n",
    "    ##---------------------------\n",
    "    #     定义参数先验，包括 beta_0，beta_1，sigma\n",
    "    #---------------------------\n",
    "    beta_0 = ...       \n",
    "    beta_1 = ...\n",
    "    beta_2 = ...\n",
    "    beta_3 = ...\n",
    "    sigma = ...\n",
    "\n",
    "    stress = pm.MutableData(\"stress\",df.stress, dims=\"obs_id\")      #stress是自变量压力水平\n",
    "    smoke = pm.MutableData(\"smoke\",df.smoke, dims=\"obs_id\")         #smoke是自变量吸烟水平\n",
    "    ##---------------------------\n",
    "    #     定义回归模型\n",
    "    #---------------------------\n",
    "    mu = pm.Deterministic(\"mu\", ..., dims=\"obs_id\")      #定义mu，将自变量与先验结合\n",
    "\n",
    "    ##---------------------------\n",
    "    #     定义似然函数\n",
    "    #---------------------------\n",
    "    likelihood = pm.Normal(\"y_est\", mu=..., sigma=..., observed=..., dims=\"obs_id\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务2：拟合模型并进行 MCMC 检查"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta_0, beta_1, beta_2, beta_3, sigma]\n"
     ]
    },
    {
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      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 10 seconds.\n"
     ]
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     对模型 model6 进行 MCMC 采样\n",
    "#     注意！！！以下代码可能需要运行1-2分钟左右\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>beta_0</th>\n",
       "      <td>55.702</td>\n",
       "      <td>2.518</td>\n",
       "      <td>50.968</td>\n",
       "      <td>60.494</td>\n",
       "      <td>0.026</td>\n",
       "      <td>0.018</td>\n",
       "      <td>9734.0</td>\n",
       "      <td>9482.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_1</th>\n",
       "      <td>-0.405</td>\n",
       "      <td>0.062</td>\n",
       "      <td>-0.521</td>\n",
       "      <td>-0.286</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>9689.0</td>\n",
       "      <td>8801.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_2</th>\n",
       "      <td>0.758</td>\n",
       "      <td>7.125</td>\n",
       "      <td>-12.268</td>\n",
       "      <td>14.453</td>\n",
       "      <td>0.070</td>\n",
       "      <td>0.058</td>\n",
       "      <td>10489.0</td>\n",
       "      <td>10679.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_3</th>\n",
       "      <td>-0.068</td>\n",
       "      <td>0.186</td>\n",
       "      <td>-0.430</td>\n",
       "      <td>0.267</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>10353.0</td>\n",
       "      <td>10588.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mu[0]</th>\n",
       "      <td>40.329</td>\n",
       "      <td>0.445</td>\n",
       "      <td>39.526</td>\n",
       "      <td>41.200</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>19487.0</td>\n",
       "      <td>16883.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mu[170]</th>\n",
       "      <td>38.711</td>\n",
       "      <td>0.452</td>\n",
       "      <td>37.889</td>\n",
       "      <td>39.580</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>20697.0</td>\n",
       "      <td>17363.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mu[171]</th>\n",
       "      <td>38.711</td>\n",
       "      <td>0.452</td>\n",
       "      <td>37.889</td>\n",
       "      <td>39.580</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>20697.0</td>\n",
       "      <td>17363.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mu[172]</th>\n",
       "      <td>39.925</td>\n",
       "      <td>0.434</td>\n",
       "      <td>39.138</td>\n",
       "      <td>40.767</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>21100.0</td>\n",
       "      <td>16794.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mu[173]</th>\n",
       "      <td>42.352</td>\n",
       "      <td>0.605</td>\n",
       "      <td>41.215</td>\n",
       "      <td>43.492</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>12929.0</td>\n",
       "      <td>14035.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>5.469</td>\n",
       "      <td>0.292</td>\n",
       "      <td>4.933</td>\n",
       "      <td>6.017</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>14140.0</td>\n",
       "      <td>11703.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>179 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "beta_0   55.702  2.518  50.968   60.494      0.026    0.018    9734.0   \n",
       "beta_1   -0.405  0.062  -0.521   -0.286      0.001    0.000    9689.0   \n",
       "beta_2    0.758  7.125 -12.268   14.453      0.070    0.058   10489.0   \n",
       "beta_3   -0.068  0.186  -0.430    0.267      0.002    0.001   10353.0   \n",
       "mu[0]    40.329  0.445  39.526   41.200      0.003    0.002   19487.0   \n",
       "...         ...    ...     ...      ...        ...      ...       ...   \n",
       "mu[170]  38.711  0.452  37.889   39.580      0.003    0.002   20697.0   \n",
       "mu[171]  38.711  0.452  37.889   39.580      0.003    0.002   20697.0   \n",
       "mu[172]  39.925  0.434  39.138   40.767      0.003    0.002   21100.0   \n",
       "mu[173]  42.352  0.605  41.215   43.492      0.005    0.004   12929.0   \n",
       "sigma     5.469  0.292   4.933    6.017      0.002    0.002   14140.0   \n",
       "\n",
       "         ess_tail  r_hat  \n",
       "beta_0     9482.0    1.0  \n",
       "beta_1     8801.0    1.0  \n",
       "beta_2    10679.0    1.0  \n",
       "beta_3    10588.0    1.0  \n",
       "mu[0]     16883.0    1.0  \n",
       "...           ...    ...  \n",
       "mu[170]   17363.0    1.0  \n",
       "mu[171]   17363.0    1.0  \n",
       "mu[172]   16794.0    1.0  \n",
       "mu[173]   14035.0    1.0  \n",
       "sigma     11703.0    1.0  \n",
       "\n",
       "[179 rows x 9 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     通过可视化+统计指标检验 MCMC 是否收敛，当你顺利运行了这段代码，可以举手示意助教/老师帮助你检查其模型建立的是否正确\n",
    "#     提示：可以使用 az.az.plot_trace() 和 az.summary()函数\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务3：使用 HDI 或者 BF 进行模型推断"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     参考前面的代码计算 HDI + ROPE 区间 或者贝叶斯因子计算\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 任务4：进行后验预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [y_est]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b349a2b8b0a94106a03aaa62a3a103ee",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##---------------------------\n",
    "#     对模型进行后验预测\n",
    "#---------------------------\n",
    "with model6:\n",
    "    model6_ppc = ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##---------------------------\n",
    "#     可视化后验预测结果\n",
    "#     提示：可以使用 az.plot_ppc(...)\n",
    "#---------------------------\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 总结\n",
    "\n",
    "🤔虽然我们现在已经学习了使用不同的线性回归模型来拟合变量间的关系，但有些问题我们暂时忽略了：  \n",
    "1. 如何评估不同的模型？哪个模型最好？  \n",
    "2. 什么时候该使用什么模型？\n",
    "![Image Name](https://cdn.kesci.com/upload/image/rkz1dqyo2e.png?imageView2/0/w/960/h/960)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "接下来，我们需要对模型进行**评估**  \n",
    "\n",
    "* 我们可以从以下三个角度来思考这个问题：  \n",
    "\n",
    "    1. 模型本身公正吗？(How fair is the model?)  \n",
    "\n",
    "    2. 模型存在错误吗？(How wrong is the model?)  \n",
    "\n",
    "    3. 后验预测模型有多准确？(How accurate are the posterior predictive models?)  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型公正吗(Is the model fair?)  \n",
    "\n",
    "模型公正性是一个上位概念，它描述了模型是否符合我们(社会、道德、伦理)的预期，而不仅是关注模型和样本数据的关系。  \n",
    "\n",
    "我们可以借助几个相关问题来理解和思考模型的公众性：  \n",
    "\n",
    "1. 数据的收集过程是怎样的？  \n",
    "\n",
    "2. 数据由谁收集，数据收集的目的是什么？  \n",
    "\n",
    "3. 数据收集的过程，以及分析的结果，将对个人和社会产生什么影响？  \n",
    "\n",
    "4. 分析过程中可能会包含哪些偏见  \n",
    "    * p-hacking/HARKing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. 数据的收集的过程公平吗？**  \n",
    "\n",
    "在本示例研究中，数据来源于基于自我匹配范式的实验数据，这些数据通过线下认知实验收集而得。\n",
    "\n",
    "* 数据收集过程是公平的，被试填写了实验的知情同意书，并获得相应的报酬。  \n",
    "* 此外，数据收集过程是匿名化的，保护了被试的隐私。  \n",
    "\n",
    "极端的反例，如：  \n",
    "* 在数据收集过程中，仅选取大学生群体作为样本，而忽略其他重要的人群。\n",
    "\n",
    "🤔基于这些数据的模型公正吗？  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. 研究目的，以及数据收集的目的公平吗？**  \n",
    "\n",
    "在本示例研究中，研究目的来源自心理学家的好奇和假设。这是合理的，因为心理学研究是一种探索性的研究方法。  \n",
    "\n",
    "一些极端的反例：  \n",
    "* 如果研究项目来源于开发缓解压力药的厂商。那么，研究目的就可能被操纵，以支持药厂的销售。  \n",
    "* 例如，有目的的选择被试。  \n",
    "* 例如，有目的性的将实验目告诉被试，从而收集到符合预期的数据。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. 模型分析的结果，将对个人和社会产生什么影响？**  \n",
    "\n",
    "在本示例研究中，研究结果(模型分析的结果)具有一定的理论意义和实际意义。  \n",
    "* 在理论层面， 自我匹配范式中的模型能够帮助揭示个体如何处理与“自我”相关的信息。\n",
    "* 在实际意义层面，通过这些模型，可以更精确地识别个体在自我认知过程中的偏差。 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. 分析过程中包含的偏见？**  \n",
    "\n",
    "一些反例：  \n",
    "* 假设在一次研究中使用多种问卷收集多种因变量，然后选择有相关性的变量进行报告?  \n",
    "* 在多因素实验设计中，通过增加变量来获得显著的交互作用，并尝试多种简单效应分析。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在心理学研究中，模型公正性往往与***心理学研究的可重复性***相关。  \n",
    "\n",
    "1. 数据的收集过程是怎样的？  \n",
    "\n",
    "2. 数据由谁收集，数据收集的目的是什么？  \n",
    "\n",
    "3. 数据收集的过程，以及分析的结果，将对个人和社会产生什么影响？  \n",
    "\n",
    "4. 分析过程中可能会包含哪些偏见  \n",
    "    * p-hacking/HARKing  \n",
    "\n",
    "<div style=\"text-align: center;\">\n",
    "    <img src=\"https://pic2.zhimg.com/80/v2-778de6c621356bc2c23c3a09ff2b0be5_1440w.webp\" \n",
    "         alt=\"Image Description\" \n",
    "         style=\"width: 60%; height: auto;\">\n",
    "</div>\n",
    "\n",
    "(来源：胡传鹏, ..., 彭凯平. (2016). 心理学研究中的可重复性问题:从危机到契机. 心理科学进展(9), 15.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "虽然贝叶斯模型无法直接回答“模型是否公平”这个问题，但它能更好地整合前提假设和先验知识。通过模型比较的方式，贝叶斯方法可以帮助我们发现模型中的潜在错误，以及模型的预测能力。🔍\n",
    "\n",
    "模型公正的三大思考角度：\n",
    "1. 模型本身公平吗？ 🤔\n",
    "2. 模型有错误吗？ ❌\n",
    "3. 后验预测模型有多准确？ 🎯"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 这个模型可能有多错误(How wrong is the model?)  \n",
    "\n",
    "\n",
    ">  **<center>“all models are wrong, but some are useful.   ————George Box”</center>**  \n",
    "\n",
    "\n",
    "* 尽管统计模型是对更复杂现实的简化表达，良好的统计模型仍然可以是有用的，并可以增进我们对世界复杂性的理解。  \n",
    "\n",
    "* 因此，在评估模型时，要问的下一个问题不是模型是否错误(is the model wrong?)，而是模型错误的程度(How wrong is the model?)  \n",
    "\n",
    "🤔思考贝叶斯线性回归模型的假设在多大程度上与现实相符？\n",
    "\n",
    "\n",
    "**在贝叶斯中，模型评估主要会通过绝对指标和相对指标来进行评估，我们会在下一节课详细介绍。**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_id": "11121B94841F40B4AD09F0DE3570342F",
    "id": "2EA18F9E553D406B94265819EE6F2A36",
    "jupyter": {},
    "notebookId": "655b69f19f41eb29b96aa415",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**概念区别：模型诊断(model diagnostic) vs. 模型验证(model validation)**  \n",
    "\n",
    "在贝叶斯的workflow中，  \n",
    "\n",
    "- MCMC评估是对MCMC进行检验，在Gelman et al (2020)中也被称为计算过程的验证(validate computation)，其核心在于确定MCMC算法采样得到的样本是否足以提供目标分布的精确近似。  \n",
    "\n",
    "- 模型评估则是指对模型是否公平性、有效性、可信性进行评估，既可以是对单个模型，也可以是对多个模型进行。  \n",
    "\n",
    "理想情况下，两种评估结果都是良好的。然而，情况并非总是如此。  \n",
    "  - 我们可能有一个很好的模型框架，但是MCMC链的结果却不稳定，进而导致不准确的后验近似。  \n",
    "  - 或者刚好相反，我们可以获得很好地后验近似，但模型本身却并不反映任何事实。  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/image/rkz1dqyo2e.png?imageView2/0/w/960/h/960)"
   ]
  }
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